Question

A student must choose one of the subjects, art, geology, or psychology, as an elective. She is equally likely to choose art or psychology and twice as likely to choose geology. What are the respective probabilities that she chooses art, geology, and psychology?

Answer 1

P (arts) = 0.25

P (psychology) = 0.25

P (geology) = 0.5

Explanation:

Let the probability of choosing art = x

As given that she is equally likely to choose art or psychology and twice as likely to choose geology.

So,

P (arts) = x = P (psychology)

P (geology) = 2x

The sum of the probability = 1

So,

P (arts) + (psychology) + P (geology) = 1

x + x + 2x = 1

x = 0.25

P (arts) = x = 0.25

P (psychology) = x = 0.25

P (geology) = 2x = 2*0.25 = 0.5