I will be attempting the below:
CHAPTER 1. DISCRETE PROBABILITY DISTRIBUTIONS
Exercise 8
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:
She must chooese only one out of Art, Psychology or Geology, the Probability = 1.
P(A) - Probability of choosing Art P(P) - Probability of choosing Psychology P(G) - Probability of choosing Geology
P(A) + P(P) + P(G) = 1
She is equally likely to choose art or psychology and twice as likely to choose geology. Since there is no overlap of probability
x + x + 2x = 1
x = 1/4 = P(A) = P(P)
P(G) = 1/2