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
• B. 0.352
• C. 0.255
• D. 0.225

Answer 1

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
$\begin{array}{ccc}P\left(A\right)& =& P\left(A\right|B\left)P\right(B)+P(A|B\text{'})P(B\text{'})\\ & =& 0.25\times 0.75+0.15\times 0.25\\ & =& 0.1875+0.0375\\ & =& 0.225\end{array}$