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Probability

Long Answer Type

881. Probabilities of solving a specific problem independently by A and B are

1 half space and space 1 third

respectively. If both try to solve the problem independently, find the probability:
(i) the problem is solved (ii) exactly one of them solves the problem.

175 Views

Short Answer Type

882. The probability that A will solve a problem is

2 over 5

and B will solve it is

5 over 6

. If both try the problem independently, find the probability that the problem will be solved.

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883. A problem of Mathematics is given to three students, whose chances of solving it are

1 third comma space 1 fourth comma space 1 fifth.

What is the probability that the problem will be solved?

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884. In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.
Find the probability that she reads neither Hindi nor English newspaper.

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885. In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.
If she reads Hindi newspaper, find the probability that she reads English newspaper.

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886. In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.
If she reads English newspaper, find the probability that she reads Hindi newspaper.

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887. A certain team wins with probability 0.7, losses with probability 0.2 and ties with probability 0.1. The team plays three games. Find the probability that the team wins at least two of the games, but not lose.

Let W , L and T denote the events that the team wins, loses and ties respectively.
∴ P (W) = 0.7, P (L) = 0.2, P (T) = 0.1
Required probability = P (team wins at least two games but not loses)
= P (WWT) + P (WTW) + P (TWW) + P (WWW)
= P (W) P (W) P (T) + P (W) P (T) P (W) + P (T) P (W) P (W) + P(W) P(W) P(W)
= 3 [P (W) P (W) P (T)] + P (W) P (W) P (W)
= 3 [(0.7) (0.7) (0.1) + (0.7) (0.7) (0.7)
= 3 × 0.049 + 0.343 = 0.147 + 0.343
= 0.49

254 Views

888.

A can hit a target 4 times in 5 shots, B 3 times in 4 shots, and C 2 times in 3 shots. Calculate the probability that
(i) A B, C all may hit (ii) B, C may hit and A may lose.

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889. A can hit a target 3 times in 5 shots, B 2 times in 5 shots, C 3 times in 4 shots. Each fire a volley, what is the probability that 2 shots hit the target?

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890. A can hit a target 4 times with 5 shots. B can hit 3 times with 5 shots and C can hit 3 times with 5 shots. Each fire a volley, what is the probability that 2 shots hit the target?

168 Views