An integer is chosen from the first 200 integers. Find the proba
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    Probability

    Multiple Choice QuestionsLong 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. 

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    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?
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    Multiple Choice QuestionsShort 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.
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    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
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    Multiple Choice QuestionsLong 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
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    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. 

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    Multiple Choice QuestionsShort Answer Type

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

    straight n left parenthesis straight S right parenthesis space equals space straight C presuperscript 200 subscript 1 space equals space 200                      [∵ There are two hundred integers, out of which one is chosen]

    (a) Event A: The integer chosen is divisible by 6.
    rightwards double arrow                         A = {6, 12, 18, ........, 198}
    rightwards double arrow                      straight n left parenthesis straight A right parenthesis space equals space straight C presuperscript 33 subscript 1 space equals space 33

    ∴                        <pre>uncaught exception: <b>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</b><br /><br />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<br />#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 integer chosen is divisible by 8.
    rightwards double arrow                        B = {8, 16, 24, ......., 200}
    rightwards double arrow                      straight n left parenthesis straight B right parenthesis space equals space straight C presuperscript 25 subscript 1 space equals space 25
    ∴                     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 S right parenthesis end fraction equals 25 over 200.

    Event left parenthesis straight A intersection straight B right parenthesis : The integer chosen is divisible by 6 and 8 i.e, by the l.c.m 24.
    rightwards double arrow                       space space left parenthesis straight A intersection straight B right parenthesis space equals space left curly bracket 24 comma space 48 comma space 72 comma space........ comma space 192 right curly bracket
    rightwards double arrow                      straight n left parenthesis straight A intersection straight B right parenthesis space equals space straight C presuperscript 8 subscript 1 equals 8
    ∴                       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 8 over 200

    Now,         straight P left parenthesis straight A intersection straight B right parenthesis space not equal to space 0 rightwards double arrow Events A and B are not mutually exclusive.
    rightwards double arrow            <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>
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    Multiple Choice QuestionsLong 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.
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    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.
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    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.
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