Question

There are 5 students who play guitar in class XI and 8 students who play guitar in class XII. Each class has 50 students. The probability of choosing class XI is $\frac{2}{5}$ and the probability of choosing class XII is $\frac{3}{5}$. A student is chosen and is found to be playing guitar. If the probability that the chosen student is from class XI is p, then the value of 34p is equal to

• A. 10
• B. 20
• C. 5
• D. 15

Answer 1

The correct option is A 10

Let A be the event that class XI is chosen and B be the event that class XII is chosen. Let G be the event student chosen plays guitar.
Let us write down the probabilities given in the question
Probability of choosing class XI = P(A) = $\frac{2}{5}$
Probability of choosing class XII = P(B) = $\frac{3}{5}$
Probability of a student from class XI plays guitar $=P\left(\frac{G}{A}\right)=\frac{5}{50}$
Probability of a student from class XII plays guitar $=P\left(\frac{G}{B}\right)=\frac{8}{50}$
We want to find probability that the chosen student is from class XI given that he/she plays guitar or $=P\left(\frac{A}{G}\right)$
This is given by
$=P\left(\frac{A}{G}\right)=\frac{P\left(A\right)P\left(\frac{G}{A}\right)}{P\left(A\right)P\left(\frac{G}{A}\right)+P\left(B\right)P\left(\frac{G}{B}\right)}$
Substituting the values we get
$=P\left(\frac{A}{G}\right)=\frac{\frac{2}{5}\times \frac{5}{50}}{\frac{2}{5}\times \frac{5}{50}\times \frac{3}{5}\times \frac{8}{50}}=\frac{10}{34}\Rightarrow 34P\left(\frac{A}{G}\right)=10$