During a job interview, the probability of a candidate having a B.Tech degree was $\frac{5}{12}$ while the probability of a candidate having an MBA degree was $\frac{7}{16}$. The probability of a candidate having a B.Tech degree or an MBA degree or both is $\frac{11}{24}$. What is the probability of a candidate having a B.Tech degree given that the candidate has an MBA degree?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{19}{21}$ ##
Given that,
The probability of B. Tech degree $P(A) = \frac{5}{12}$
Probability of MBA degree $P(B) = \frac{7}{16}$
Probability of B.Tech or MBA degree $P(A \cup B) = \frac{11}{24}$
We know that $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$P(A \cap B) = \frac{20 + 21 - 22}{48} = \frac{19}{48}$
Now,
$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{19}{48}}{\frac{7}{16}} = \frac{19}{21}$