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Mathematics : Probability

Long Answer Type

871.

The probability of A solving a problem is $3 over 7$ and that of B solving it is $1 third.$ What is the probability that
(i) at least one of them will solve the problem?
(ii) Only one of them will solve the problem?

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Short Answer Type

872. A speaks truth in 60% cases and B in 90% cases. In what percentage of cases are they likely to contradict each other in stating the same fact.

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873. A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?

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874. The probability of hitting a target by three marksmen are

1 half comma space 1 third space and space 1 fourth

respectively. Find the probability that one and only one of them will hit the target when they fire simultaneously.

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875. An anti-aircraft gun can take a minimum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

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