A committee of two persons is selected from two men and two wome

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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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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

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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? 


Total members available for committee formation = 2(Men) + 2(Women) = 4
The committee consists of 2 members.
rightwards double arrow  Number of points in the sample space S = n(S) = <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>   ...(i)
(a) Event A: There is no man in the committee.
rightwards double arrow   Committee consists of 0 men (out of 2 men) and 2 women (out of 2 women)
rightwards double arrow          n(A) = <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>
Hence, P(the committee consists of no man) = 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 fraction numerator straight C presuperscript 2 subscript 0 cross times straight C presuperscript 2 subscript 2 over denominator straight C presuperscript 4 subscript 2 end fraction equals fraction numerator 1 cross times 1 over denominator 6 end fraction equals 1 over 6
(b) Event B: The committee consists of 1 man
rightwards double arrow  Committee consists of 1 man (out of 2) and 1 woman (out of 2)
rightwards double arrow        n(B) = space straight C presuperscript 2 subscript 1 cross times straight C presuperscript 2 subscript 1
Hence, P (the committee consists of 1 man and 1 woman) = P(B)
                         space equals 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 2 subscript 1 cross times straight C presuperscript 2 subscript 1 over denominator straight C presuperscript 4 subscript 2 end fraction equals fraction numerator 2 cross times 2 over denominator 6 end fraction equals 2 over 3
(c) Event C: The committee consists of 2 men
rightwards double arrow  Committee consists of 2 men (out of 2) and 0 woman (out of 2)
rightwards double arrow               n(C) = <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>
Hence, P (the committee consists of 2 men and no woman)
                  space space space space 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 2 subscript 2 cross times straight C presuperscript 2 subscript 0 over denominator straight C presuperscript 4 subscript 2 end fraction equals fraction numerator 1 cross times 1 over denominator 6 end fraction equals 1 over 6

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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 
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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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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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