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Probability

Short Answer Type

461.

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

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462.

Find the probability that a hand of 7 cards drawn from a well shuffled deck of 52 cards contain at least 3 kings.

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463.

Find the probability that a hand of 7 cards drawn from a well shuffled deck of 52 cards contain at most 3 kings.

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464. In a non-leap year, what is the probability of 52 sundays?

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465. In a leap year, what is the probability of 53 sundays?

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466. In a lottery, a person choses six different natural numbers at random from 1 to 20 and if these six numbers match with the six numbers already fixed by the lottery committee he wins the prize. What is the probability of winning the prize in the game?

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Long Answer Type

467. A lady has 8 one rupee coins, 6 two rupees coins and 7 five rupees coins in her purse. She draws one coin from the purse. Find the probability that it is:

(i) a five rupees coin. (ii) a two rupees coin.

(iii) a two rupees or a five rupees coin. (iv) not a one rupee coin,

(v) not a five rupees coin. (vi) a one rupee or two rupees coin.

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468. An urn contains 9 red, 7 white and 4 black balls. A ball is drawn at random. What is the probability that the ball drawn will be (i) red? (ii) red or black? (iii) not red?

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Short Answer Type

469. Two cards are drawn simultaneously from a pack of 52 well shuffled cards. Find the probability that both cards are aces.

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470. Two cards are drawn simultaneously from a pack of 52 well shuffled cards. Find the probability that one card is of diamond and the other is a spade.

Two cards are drawn simultaneously from a pack of 52 cards.
Number of equally likely, exhaustive outcomes = n(S) = $straight C presuperscript 52 subscript 2 equals space fraction numerator 52 factorial over denominator 2 factorial space 50 factorial end fraction equals fraction numerator 52 cross times 51 over denominator 2 cross times 1 end fraction equals 26 cross times 51$
Event A: One card is diamond and the other is spade.
$rightwards double arrow$ Favourable elements are (13 diamond cards one to draw; 13 spade cards one to draw)
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P(A) = Probability that one is diamond card and other is spade card
$equals fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator 13 cross times 13 over denominator 26 cross times 51 end fraction equals 13 over 102$

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