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Probability

Short Answer Type

831. A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. Find the probability of obtaining head and an even number.

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Long Answer Type

832.

A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marbles will be
(i) blue followed by red (ii) blue and red in any order (iii) of the same colour.

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Short Answer Type

833. Two cards are drawn one by one without replacement from a well shuffled pack of 52 cards. What is the probability that one is a red card and the other is a black card?

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834. Two cards are drawn one by one without replacement from a well shuffled pack of 52 cards. What is the probability that one of the cards drawn is a king and the other a queen of the same suit?

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835.

A bag contains 4 white balls and 2 black balls. Another bag contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that both are black.

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836. An urn contains 25 balls numbered 1 to 25. Two balls are drawn from the urn with replacement. Find the probability of getting both odd numbers.

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837. An urn contains 25 balls numbered 1 to 25. Two balls are drawn from the urn with replacement. Find the probability of getting one odd and one even number.

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838. An urn contains 25 balls numbered 1 to 25. Two balls are drawn from the urn with replacement. Find the probability of getting at least one odd number .

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839. An urn contains 25 balls numbered 1 to 25. Two balls are drawn from the urn with replacement. Find the probability of getting no odd number.

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840. Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?

Let K denote the event that the card drawn is king and A be the event that the card drawn is an ace.
Now,

straight P left parenthesis straight K right parenthesis space equals space 4 over 52

Also, P(K | K) is the probability of second king with the condition that one king has already been drawn. Now there are three kings in (52 - 1) = 51 cards.

therefore space space space space space space space space space space space straight P left parenthesis straight K vertical line straight K right parenthesis space equals space 3 over 51

Again, P(A | KK) is the probability of third drawn card to be an ace, with the condition that two kings have already been drawn. Now, there arc four aces in remaining 50 cards.

therefore space space space space straight P left parenthesis straight A space vertical line space KK right parenthesis space equals 4 over 50

By multiplication law of probability, we have

straight P left parenthesis KKA right parenthesis space equals space straight P left parenthesis straight K right parenthesis space space space space space space straight P left parenthesis straight K vertical line straight K right parenthesis space space straight P left parenthesis straight A vertical line KK right parenthesis space space space space space space space space space space space space space space space equals space 4 over 52 cross times 3 over 51 cross times 4 over 50 space equals 2 over 5525

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