Find the probability that a hand of 7 cards drawn from a well sh

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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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 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:
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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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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.

 


7 cards are drawn from a well shuffled deck of 52 cards.
rightwards double arrow The number of points in sample space S = n(S) = straight C presuperscript space 52 end presuperscript subscript 7
Event A: all the four kings are drawn.
Since a total of 7 cards are drawn.
rightwards double arrow   4 kings are drawn out of the 4 kings and 3 cards are drawn out of the remaining 48.
rightwards double arrow      straight n left parenthesis straight A right parenthesis space equals space straight C presuperscript 4 subscript 4 space cross times space straight C presuperscript 48 subscript 3 space equals space 1 cross times straight C presuperscript 48 subscript 3 space equals space straight C presuperscript 48 subscript 3
rightwards double arrow      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 48 subscript 3 over denominator straight C presuperscript 52 subscript 7 end fraction equals fraction numerator 48 factorial over denominator 45 factorial space 3 factorial end fraction cross times fraction numerator 45 factorial space 7 factorial over denominator 52 factorial end fraction equals fraction numerator 48 factorial space 7 factorial over denominator 3 factorial space 52 factorial end fraction equals fraction numerator 7 cross times 6 cross times 5 cross times 4 over denominator 52 cross times 51 cross times 50 cross times 49 end fraction equals 1 over 7735

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