Ex. 8, p.36.

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?

Solution:

         (Chances for)
 P(x) = ---------------
        (Total chances)

P(Art) = x

P(Psychology) = x

P(Geology) = 2x

As student must choose ONE of the subjects, the total probability is equal to 1:

P(Art) + P(Psychology) + P(Geology) = 1

x + x + 2x = 1

Hence, the respective probabilities are the following:

P(Art) = 1/4

P(Psychology) = 1/4

P(Geology) = 1/2

Ex. 12, p.36

You offer 3 : 1 odds that your friend Smith will be elected mayor of your city. What probability are you assigning to the event that Smith wins?

Solution

Odds:

(Chances for) : (Chances against)

P(win) = 3/1 : 4/1 = 3/4 = 0.75