One card is drawn from a well shuffled deck of 52 cards. If the

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 Multiple Choice QuestionsShort Answer Type

451. A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is 12.
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452. A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is greater than 5.
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453. A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed, find the probability that the sum of numbers that turn up is less than 6.
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454. A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed, find the probability that the sum of numbers that turn up is 3 or 12.
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 Multiple Choice QuestionsLong Answer Type

455. A committee of two persons is selected from two men and two women. What is the probability that the committee will have:
(a) no man? (b) one man? (c) two men? 
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456. One card is drawn from a well shuffled deck of 52 cards. If the each outcome is equally likely, calculate the probability that the card will be:
(i) a diamond                                                      (ii) not an ace
(iii) a black card                                                  (iv) not a diamond
(v) not a black card 


One card is drawn from a deck of 52 cards.
rightwards double arrow Number of points in the sample space S = n(S) = straight C presuperscript 52 subscript 1 equals 52.
(i) Event A: the card drawn is a diamond.
rightwards double arrow             n(A) = straight C presuperscript 13 subscript 1 space left parenthesis one space out space of space 13 space diamond space cards right parenthesis
Hence,      space space straight P left parenthesis straight A right parenthesis space equals space fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 13 subscript 1 over denominator straight C presuperscript 52 subscript 1 end fraction equals 13 over 52 equals 1 fourth

(ii) Event B: the card drawn is not an ace.
rightwards double arrow        n(B) = C presuperscript 48 subscript 1                   [∵ there are 4 aces, so number of remaining cards = 52 - 4 = 48]
Hence,    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 fraction numerator straight C presuperscript 48 subscript 1 over denominator straight C presuperscript 52 subscript 1 end fraction equals 48 over 52 equals 12 over 13

(iii) Event C: the card drawn is a black card.
rightwards double arrow        n(C) = straight C presuperscript 26 subscript 1 (one out of 26 black cards)
Hence,    straight P left parenthesis straight C right parenthesis equals fraction numerator straight n left parenthesis straight C right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 26 subscript 1 over denominator straight C presuperscript 52 subscript 2 end fraction equals 26 over 52 equals 1 half

(iv) Event D: the card drawn is a diamond card.
rightwards double arrow        n(D) = straight C presuperscript 13 subscript 1 (one out of 13 diamond cards)
rightwards double arrow        P(D) = fraction numerator straight n left parenthesis straight D right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 13 subscript 1 over denominator straight C presuperscript 52 subscript 1 end fraction equals 13 over 52 equals 1 fourth
We have to find the probability that the card is not a diamond card i.e. straight P left parenthesis straight D with bar on top right parenthesis.
Now,   straight P left parenthesis top enclose straight D right parenthesis space equals space 1 minus straight P left parenthesis straight D right parenthesis space equals space 1 minus 1 fourth equals 3 over 4
Hence, P (card drawn is not a diamond card) = <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)
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#6 {main}</pre>
(v) Event E: the card drawn is a black card
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)
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#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...')
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#6 {main}</pre>
            straight P left parenthesis top enclose straight E right parenthesis space equals space straight P (the card drawn is not a black card) = 1 - P(E) = <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...')
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#6 {main}</pre>

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 Multiple Choice QuestionsShort Answer Type

457. A card is selected from a pack of 52 cards. How many points are there in the sample space?
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458. A card is selected from a pack of 52 cards. Calculate the probability that the card is an ace of spade.
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459. A card is selected from a pack of 52 cards. Calculate the probability that the card is (i) an ace (ii) black card.
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460.

Find the probability that a hand of 7 cards drawn from a well shuffled deck of 52 cards contain all the four kings.

 

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