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Probability

Short Answer Type

891.

A and B toss a coin alternatively till one of them gets a head and wins the game. If A starts the game, find the probability of his winning at his third toss.

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Long Answer Type

892. A and B throw a die alternately till one of them gets a ‘6’ and wins the game. Find their respective probabilities of winning if A starts first.

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893. A and B toss a coin alternately till one of them gets a head and wins the game, if A starts first, find the probability that B will win the game.

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894. A and B take turn in throwing two dice. The first to throw sum 9 being awarded. Show that if A has the first throw, their chances of winning are in the ratio 9:8.

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895. Two persons throw a die alternatively till one of them gets a three and wins the game. Find their respective probability of winning.

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Short Answer Type

896. There are three urns A, B and C. Urn A contains 4 white balls and 5 blue balls. Urn B contains 3 white balls and 4 blue balls. Urn C contains 3 white balls and 6 blue balls. One ball is drawn from each of these urns. What is the probability that out of these three balls drawn, two are white balls and one is a blue ball?

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897.

There are three urns A, B and C. Urn A contains 4 white balls and 5 blue balls. Urn B contains 4 white balls and 3 blue balls. Urn C contains 2 white balls and 4 blue balls. One half is drawn from each of these urns. What is the probability that out of these three balls drawn, two are white balls and one is a blue ball?

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898. In bag A, there are 5 white and 8 red balls, in bag B, 7 white and 6 red balls and in bag C, 6 white and 5 red balls. One ball is taken out at random from each bag. Find the probability that all the three balls are of the same colour.

Bag A Bag B Bag C
White 5 7 6
Red 8 6 5
P(all three balls of the same colour) = P(all white or all red)
= P(all white) + P(all red)
= P(WWW) + P(RRR)
= P(W) P(W) P(W) + P(R) P(R) P(R)
$equals space 5 over 17 cross times 7 over 13 cross times 6 over 11 plus 8 over 13 cross times 6 over 13 cross times 5 over 11 equals space 210 over 1859 plus 240 over 1859 space equals space 450 over 1859.$

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899. A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike, and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

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900.

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

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