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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.

(i) The probabilities of A and B solving the problem are

1 half space and space 1 third

respectively.
i.e.

straight P left parenthesis straight A right parenthesis space equals 1 half comma space space straight P left parenthesis straight B right parenthesis space equals space 1 third

therefore

the probabilities of A and B solving the problems are

1 minus 1 half comma space space 1 minus 1 third.

i.e.,

1 half comma space 2 over 3

respectively.

therefore

probability that problem is not solved by A and B =

1 half cross times 2 over 3 space equals space 1 third

therefore

probability that the problem is solved =

1 minus 1 third equals space space 2 over 3

(ii) P(exactly one of them solves the problem)

equals space straight P left parenthesis straight A space straight B with bar on top space space or space space straight A with bar on top space straight B right parenthesis space equals space straight P left parenthesis straight A space straight B with bar on top right parenthesis space plus space left parenthesis straight A with bar on top space straight B right parenthesis equals space straight P left parenthesis straight A right parenthesis thin space straight P left parenthesis straight B with bar on top right parenthesis space plus space straight P left parenthesis straight A with bar on top right parenthesis thin space straight P left parenthesis straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space left square bracket 1 space minus space straight P left parenthesis straight B right parenthesis right square bracket space plus space left square bracket 1 space minus space straight P left parenthesis straight A right parenthesis right square bracket space straight P left parenthesis straight B right parenthesis space equals space open parentheses 1 half close parentheses space open square brackets 1 minus 1 third close square brackets space plus space open square brackets 1 minus 1 half close square brackets space open parentheses 1 third close parentheses space equals space 1 half cross times 2 over 3 cross times 1 half cross times 1 third space equals space 1 third plus 1 over 6 space equals fraction numerator 2 plus 1 over denominator 6 end fraction space equals 3 over 6 space equals 1 half space

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.

90 Views

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?

82 Views

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.

72 Views

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.

76 Views

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.

81 Views

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.

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.

93 Views

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?

97 Views

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