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Probability

Short 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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Long 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

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Short 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.

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.
$rightwards double arrow$ $straight n left parenthesis straight A right parenthesis space equals space straight C presuperscript 4 subscript 4 space cross times space straight C presuperscript 48 subscript 3 space equals space 1 cross times straight C presuperscript 48 subscript 3 space equals space straight C presuperscript 48 subscript 3$
$rightwards double arrow$ $straight P left parenthesis straight A right parenthesis space equals space fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 48 subscript 3 over denominator straight C presuperscript 52 subscript 7 end fraction equals fraction numerator 48 factorial over denominator 45 factorial space 3 factorial end fraction cross times fraction numerator 45 factorial space 7 factorial over denominator 52 factorial end fraction equals fraction numerator 48 factorial space 7 factorial over denominator 3 factorial space 52 factorial end fraction equals fraction numerator 7 cross times 6 cross times 5 cross times 4 over denominator 52 cross times 51 cross times 50 cross times 49 end fraction equals 1 over 7735$