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Question

A marksman is standing in front of a target participating in the regional championships. The probability of no foul happening is 75%. The chances that he hits the bullseye given there is no foul are 25%, while the chances of hitting bullseye with a foul are 15%. Find the probability of him hitting the bullseye.

A
0.245
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B
0.352
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C
0.255
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D
0.225
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Solution

The correct option is D 0.225
Let A be the event that marksman hits the bullseye.
Let B be the event that there is no foul.
Then P(B) = 0.75
and P(B') = 1 - 0.75 = 0.25

Given P(A|B) = 0.25
and P(A|B') = 0.15

As B and B' form a partition of the sample space, therefore, by theorem of total probability, we have
P(A) = P(A|B) P(B) + P(A|B') P(B')= 0.25×0.75 + 0.15×0.25= 0.1875 + 0.0375= 0.225

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