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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.

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.

Let A and B be two events such that
A : a student reads Hindi newspaper
B : a student reads English newspaper.
$therefore space space space space space straight P left parenthesis straight A right parenthesis space equals space 60 over 100 space equals 3 over 5 comma space space space space straight P left parenthesis straight B right parenthesis space equals space 40 over 100 space equals space 2 over 5 space space space space space space space space space space space straight P left parenthesis straight A space intersection space straight B right parenthesis space equals space 20 over 100 space equals 1 fifth$
P(student reads neither Hindi nor English newspaper)
$equals space straight P left parenthesis straight A to the power of straight c space and space straight B to the power of straight c right parenthesis space equals space straight P space open square brackets open parentheses straight A space union space straight B close parentheses to the power of straight c close square brackets space equals space 1 space space minus space straight P left parenthesis straight A space union space straight B right parenthesis space equals space 1 minus open square brackets straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A space intersection space straight B right parenthesis close square brackets space equals space 1 minus open square brackets 3 over 5 plus 2 over 5 minus 1 fifth close square brackets space equals space 1 minus 4 over 5 space equals space 1 fifth$

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