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Probability

Short Answer Type

471. Two cards are drawn simultaneously from a pack of 52 well shuffled cards. Find the probability that both cards are red.

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472. Two cards are drawn simultaneously from a pack of 52 well shuffled cards. Find the probability that one card is red and one is black.

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473. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.

122 Views

474. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets.

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475. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy ten tickets.

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476.

In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win one prize.

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477. In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win two prizes?

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478. In a lottery, there are 35 tickets in all, 10 bearing prize numbers and 25 are blanks. A lady draws 2 tickets at random. What is the probability that she will win no prize?

98 Views

Long Answer Type

479.
A bag contains 3 red balls bearing numbers 1, 2, 3 (one number on one ball) ; and two black balls bearing numbers 4 and 6. A ball is drawn, its number noted and the ball is replaced in the bag. Then another ball is drawn and its number noted. Find the probability of drawing:

(i) 2 on the first draw and 6 on the second draw.

(ii) a number ≤ 2 on the first draw and 4 on the second draw.

(iii) a total of 5.

The balls are drawn with replacement.
∴ The sample space,

S = $open curly brackets table row cell left parenthesis 1 comma 1 right parenthesis comma end cell cell left parenthesis 1 comma 2 right parenthesis comma end cell cell left parenthesis 1 comma 3 right parenthesis comma end cell cell left parenthesis 1 comma 4 right parenthesis comma end cell cell left parenthesis 1 comma 6 right parenthesis end cell row cell left parenthesis 2 comma 1 right parenthesis comma end cell cell left parenthesis 2 comma 2 right parenthesis comma end cell cell left parenthesis 2 comma 3 right parenthesis comma end cell cell left parenthesis 2 comma 4 right parenthesis comma end cell cell left parenthesis 2 comma 6 right parenthesis end cell row cell left parenthesis 3 comma 1 right parenthesis comma end cell cell left parenthesis 3 comma 2 right parenthesis comma end cell cell left parenthesis 3 comma 3 right parenthesis comma end cell cell left parenthesis 3 comma 4 right parenthesis comma end cell cell left parenthesis 3 comma 6 right parenthesis end cell row cell left parenthesis 4 comma 1 right parenthesis comma end cell cell left parenthesis 4 comma 2 right parenthesis comma end cell cell left parenthesis 4 comma 3 right parenthesis comma end cell cell left parenthesis 4 comma 4 right parenthesis comma end cell cell left parenthesis 4 comma 6 right parenthesis end cell row cell left parenthesis 5 comma 1 right parenthesis end cell cell left parenthesis 5 comma 2 right parenthesis end cell cell left parenthesis 5 comma 3 right parenthesis comma end cell cell left parenthesis 5 comma 4 right parenthesis comma end cell cell left parenthesis 5 comma 6 right parenthesis end cell end table close curly brackets$

$rightwards double arrow$ n(S) = 25
(i) Event A: 2 is drawn in the first draw and 6 in the second draw.
$rightwards double arrow$ A = {(2,6)} $rightwards double arrow$ n(A) = 1
∴ P(2 on the first and 6 on the second) = P(A) = $fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 1 over 25$

(ii) Event B : a number $less or equal than$ 2 in the first draw and 4 in the second draw.
$rightwards double arrow$ B = {(1,4), (2,4)} $rightwards double arrow$ n(B) = 2
∴ P(number $less or equal than$ 2 in the first and 4 in the second draw) = P(B) = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

(iii) Event C: a total of 5 is obtained
$rightwards double arrow$ C = {(1,4), (2,3), (3,2), (4,1)}
$rightwards double arrow$ n(C) = 4

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

189 Views

Short Answer Type

480. The number lock of a suitcase has 4 wheels, each labelled with 10 digits i.e., from 0 to 9. The lock opens with a sequence of 4 digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

127 Views