In a leap year, what is the probability of 53 sundays? from Mat

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 Multiple Choice QuestionsShort 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?


A leap year has 366 days = 52 weeks + 2 days
The event of 53 sundays depends upon the remaining 2 days.
Possible outcomes from remaining 2 days are:
S = {Sunday/Monday, Monday/Tuesday, Tuesday/Wednesday, Wednesday/Thursday, Thursday/Friday, Friday/Saturday, Saturday/Sunday}
rightwards double arrow                        n(S) = 7
Event B: The year has 53 sundays
rightwards double arrow                         B = {Sunday/Monday, Satruday/Sunday}
                                                                 (Since we require 1 more sunday to make it 53)
rightwards double arrow                      n(B) = m = 2
rightwards double arrow                      P(B) = probability of 53 Sundays in leap year = fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 2 over 7

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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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 Multiple Choice QuestionsLong 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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 Multiple Choice QuestionsShort 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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