Question

. The Probability that Ram will hit a target is 0.56 and the Probability that Shyam will hit the target is 0.45. The Probability that both will hit the target is 0.25. Find the Probability that
i) at least one will hit the target
ii) exactly one will hit the target
iii) not more than will hit the target

Answer 1

Answer on Question #44830 – Math – Statistics and Probability

Question

The Probability that Ram will hit a target is 0.56 and the Probability that Shyam will hit the target is 0.45. The Probability that both will hit the target is 0.25. Find the Probability that i) at least one will hit the target

ii) exactly one will hit the target

iii) not more than one will hit the target.

Solution

Let the event $A$ is that Ram hit a target, $B$ is that Shyam hit the target.

Then $P(A) = 0.56, P(B) = 0.45, P(A \cap B) = 0.25$.

i) $P\{ \text{at least one will hit the target} \} = P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.56 + 0.45 - 0.25 = 0.76.$

ii) $P\{ \text{exactly one will hit the target} \} = P(A \setminus B) + P(B \setminus A) = P(A) - P(A \cap B) + P(B) - P(A \cap B) = 0.56 - 0.25 + 0.45 - 0.25 = 0.51.$

iii) $P\{ \text{not more than one will hit the target} \} = 1 - P(A \cap B) = 1 - 0.25 = 0.75.$

Answer.

i) 0.76

ii) 0.51

iii) 0.75

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