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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.

One card is drawn from a deck of 52 cards.
$rightwards double arrow$ Number of points in the sample space S = n(S) = $straight C presuperscript 52 subscript 1 equals 52.$
Event A = the card is an ace (one out of 4 aces)
$rightwards double arrow$ n(A) = $straight C presuperscript 4 subscript 1$
Hence, $straight P left parenthesis straight A right parenthesis space equals space fraction numerator straight C presuperscript 4 subscript 1 over denominator straight C presuperscript 52 subscript 1 end fraction equals 4 over 52 equals 1 over 13$
Hence, the probability of getting an ace = $1 over 13$
Event B: the card drawn is a black card. (one out of 26 black cards)
$rightwards double arrow$ n(B) = $straight C presuperscript 26 subscript 1$
$rightwards double arrow$ $space space straight P left parenthesis straight B right parenthesis space equals space fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 26 subscript 1 over denominator straight C presuperscript 52 subscript 1 end fraction equals 26 over 52 equals 1 half$

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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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