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Probability

Short Answer Type

411.

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State whether the following is true or false (give reason for your answer):
A and B' are mutually exclusive.

112 Views

412.

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State whether the following is true or false (give reason for your answer):
A', B' C are mutually exclusive and exhaustive.

119 Views

Long Answer Type

413.
From a group of 2 boys and 3 girls, two children selected at random. Describe the events:

A : Both children are girls.

B : The selected group consists of one boy and one girl.

C : The group consists of atleast one girl.

Find: (a) Events: B', C - A, A ∪ B,B ∩ C.

(b) Which pairs of events are mutually exclusive?

Let the boys be $straight B subscript 1 comma space straight B subscript 2$ and the girls be $space straight G subscript 1 comma space straight G subscript 2 comma space straight G subscript 3$
Two children are selected.
∴ The sample space is:
$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
A: Both children are girls.
$rightwards double arrow$ $straight A equals open curly brackets straight G subscript 1 space straight G subscript 2 comma space straight G subscript 1 space straight G subscript 3 comma space straight G subscript 2 space straight G subscript 3 close curly brackets$
B: Selected group consists of one boy and one girl.
$rightwards double arrow$ $straight B equals open curly brackets straight B subscript 1 space straight G subscript 1 comma space straight B subscript 1 space straight G subscript 2 comma space straight B subscript 1 space straight G subscript 3 comma space straight B subscript 2 space straight G subscript 1 comma space straight B subscript 2 space straight G subscript 2 comma space straight B subscript 2 space straight G subscript 3 close curly brackets$
C: Selected group consists of atleast one girl.
$rightwards double arrow$ $straight C equals open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 comma space straight G subscript 1 straight G subscript 2 comma space straight G subscript 1 straight G subscript 3 comma space straight G subscript 2 straight G subscript 3 close curly brackets$

(a) $straight B apostrophe space equals space straight S minus straight B space equals space left curly bracket straight B subscript 1 space straight B subscript 2 comma space straight G subscript 1 space straight G subscript 2 comma space straight G subscript 1 space straight G subscript 3 comma space straight G subscript 2 space straight G subscript 3 right curly bracket$
 $straight C minus straight A equals open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 comma space straight G subscript 1 straight G subscript 2 comma space straight G subscript 1 straight G subscript 3 comma space straight G subscript 2 straight G subscript 3 space close curly brackets$
 $negative open curly brackets straight G subscript 1 space straight G subscript 2 comma space straight G subscript 1 space straight G subscript 3 comma space straight G subscript 2 space straight G subscript 3 close curly brackets$
= $open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 close curly brackets$

 $straight A union straight B space equals space left curly bracket straight G subscript 1 straight G subscript 2 comma space straight G subscript 1 straight G subscript 3 comma space straight G subscript 2 straight G subscript 3 right curly bracket space union space open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 close curly brackets$
$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

 $space space space space straight B intersection straight C space equals space open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 close curly brackets$
$intersection space open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 comma space straight G subscript 1 straight G subscript 2 comma space straight G subscript 1 straight G subscript 3 comma space straight G subscript 2 straight G subscript 3 close curly brackets$
 $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ $open curly brackets straight B subscript 1 straight G subscript 1 comma space straight B subscript 1 straight G subscript 2 comma space straight B subscript 1 straight G subscript 3 comma space straight B subscript 2 straight G subscript 1 comma space straight B subscript 2 straight G subscript 2 comma space straight B subscript 2 straight G subscript 3 close curly brackets equals straight B.$
$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

(b) $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ A and B are mutually exclusive.
 $straight A intersection straight C space equals space open curly brackets straight G subscript 1 straight G subscript 2 comma space straight G subscript 1 straight G subscript 3 comma space straight G subscript 2 straight G subscript 3 close curly brackets space not equal to straight ϕ.$
 $straight B intersection straight C space equals space straight B not equal to straight ϕ.$
Hence, only events A and B are mutually exclusive.

233 Views

414.

One die is rolled. Define the sample space S of the following:

A : Getting a prime number

B : Getting an odd number

C : Getting a number less than 5

D : Getting a number divisible by 3

Use the sample space and above sets to find:

(i) A ∩ B (ii) B' (iii) C' ∩ D

(iv) A ∪ B (v) C ∩ D

110 Views

415.

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment:

A : The sum is even

B : The sum is multiple of 3

C : The sum is less than 4

D : The sum is greater than 11.

Which pairs of these events are mutually exclusive?

121 Views

Short Answer Type

416.

A coin is tossed three times. Consider the following events:

A : No head appears

B : Exactly one head appears.

C : At least two heads appear

Do they form set of mutually exclusive and exhaustive events?

116 Views

Long Answer Type

417.

A die is rolled once and the following events are described:

A : Getting a prime number on the die.

B : Getting an even number on the die.

Write the sets representing the following events.

(a) A ∩ B (b) A ∪ B (c) A-B

(d) A' ∩ B' (e) A ∪ B'

107 Views

418.

Three coins are tossed (or one coin is tossed thrice). The following events are described:

A : Getting atleast one head.

B : Getting atmost one head. Write the sets representing the following events:

(a) A ∪ B (b) A ∩ B (c) A - B

(d) A' - B.

Which of the events is a sure event and which one is impossible event ?

107 Views

419.

Two dice are rolled and the sum of numbers on them is noted. Events A, B, C, D are described as follows:

A : The sum is even.

B : The sum is a multiple of 4.

C : The sum is less than 6.

D : The sum is greater than 10.

Which pairs of the events are mutually exclusive?

104 Views

420. Two dice are rolled. Let events A, B and C be:

A : Getting a sum 10

B : Getting a sum 11

C : Getting a sum 12

(i) Is event B simple? (ii) Is event C simple? (iii) Is event A compound?

Are events B and C mutually exclusive?

108 Views