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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.

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: at least 3 kings are drawn.
$rightwards double arrow$ Either 3 kings are drawn or 4 kings are drawn.
$rightwards double arrow$ n(A) = $space straight C presuperscript 4 subscript 3 cross times straight C presuperscript 48 subscript 4 plus straight C presuperscript 4 subscript 4 cross times straight C presuperscript 48 subscript 3$

Hence, $space space straight P left parenthesis straight A right parenthesis equals fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator straight C presuperscript 4 subscript 3 cross times straight C presuperscript 48 subscript 4 plus straight C presuperscript 4 subscript 4 cross times straight C presuperscript 48 subscript 3 over denominator straight C presuperscript 52 subscript 7 end fraction equals fraction numerator straight C presuperscript 4 subscript 3 cross times straight C presuperscript 48 subscript 4 over denominator straight C presuperscript 52 subscript 7 end fraction plus fraction numerator straight C presuperscript 4 subscript 4 cross times straight C presuperscript 48 subscript 3 over denominator straight C presuperscript 52 subscript 7 end fraction equals 9 over 1547 plus 1 over 7735$
[∵ By using parts (i) and (ii)]
= $fraction numerator 45 plus 1 over denominator 7735 end fraction equals 46 over 7735$

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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.

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