Question

Three dice have the probabilities of throwing a "five" as p, q and r respectively. One of the dice is chosen at random (each is equally likely to be chosen) and thrown and a "five" appeare
D. What is the probability that the die chosen was the first one?

• A. $\frac{r}{p+q+r}$
• B. $\frac{p}{p+q+r}$
• C. $\frac{q}{p+q+r}$
• D. $\frac{p+q+r}{3}$

Hint:

When the prior probabilities are all equal (like 1/3 here), the Bayes' probability for any branch is just the likelihood of that branch divided by the sum of all likelihoods. This "equal priors" shortcut is very common in competitive exams.

Answer 1

The Correct Option is B