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Probability

Long Answer Type

531.

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that:

(a) both Anil and Ashima will not qualify the examination.
(b) at least one of them will qualify the examination.
(c) only one of them will qualfiy the examination.

339 Views

532. From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of the five persons are as follows:

S.No. Name Sex Age in Years
1. Harish M 30
2. Rohan M 33
3. Sheetal F 46
4. Alis F 28
5. Salim M 41

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson is either male or over 35 years?

Total number of persons = 5
One is selected to act as a spokes person
$rightwards double arrow$ n(A) = $straight C presuperscript 5 subscript 1 space equals space 5$
Let Event A: The person is a male.
$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Event B: The person is over 35 years
$rightwards double arrow$ $straight n left parenthesis straight B right parenthesis space equals space straight C presuperscript 2 subscript 1 equals 2$
$rightwards double arrow$ $straight P left parenthesis straight B right parenthesis space equals space fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight C right parenthesis end fraction equals 2 over 5$

Event $straight A intersection straight B colon$ The person is a male and over 35 years in age.
$rightwards double arrow$ $straight n space left parenthesis straight A intersection straight B right parenthesis space equals space straight C presuperscript 1 subscript 1 equals 1$
$rightwards double arrow$ $straight P left parenthesis straight A intersection straight B right parenthesis space equals space fraction numerator straight n left parenthesis straight A intersection straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 1 fifth$
Hence, P (either male over 35 years in age) = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
= $straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis minus straight P left parenthesis straight A intersection straight B right parenthesis space equals space 3 over 5 plus 2 over 5 minus 1 fifth equals 4 over 5$

96 Views

Short Answer Type

533. In class XI of a school 40% of the students study mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

109 Views

534. In an entrance test, that is graded on the basis of two examinations, the probability of a randomly chosen student passes the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?

108 Views

Long Answer Type

535. The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?

140 Views

536.

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that :

(i) The student opted for NCC or NSS.
(ii) The student has opted neither NCC nor NSS.
(iii) The student opted for NSS but not NCC.

165 Views

Short Answer Type

537. An integer is chosen from the first 200 integers. Find the probability that it is divisible by 6 or 8.

103 Views

Long Answer Type

538. A die is rolled twice. Find the probability that the sum of the numbers on the dice is divisible by 3 or 4.

103 Views

539. One natural number is selected at random from the first 100 natural numbers. Find the probability that it is neither divisible by 4 nor by 5.

111 Views

540. Two dice are rolled. Find the probability that the sum of the numbers on the two dice is neither divisible by 4 nor by 5.

103 Views