Question

There are 1000 students in a marching band, out of which 560 are boys. It is known that out of 560, 20% boys play trumpet. What is the probability that a student chosen randomly plays trumpet given that the chosen student is a boy?

• A. 0.35
• B. 0.25
• C. 0.15
• D. 0.2

Answer 1

The correct option is D 0.2

Let A denote the event that the student chosen plays trumpet and B be the event that the student chosen is a boy.
We have to find P(A|B).
Now,
$P\left(B\right)=\frac{560}{1000}=0.56$

Given, 20% boys play trumpet therefore,$P\left(A\cap B\right)=\frac{112}{1000}$

Then,
$\begin{array}{ccc}P\left(A\right|B)& =& \frac{P(A\cap B)}{P\left(B\right)}\\ & =& \frac{0.112}{0.56}\\ & =& 0.2\end{array}$