A runner will participate in two race events: a ten yard dash and a 50 yard dash. The runner is rated as having a 50 percent probability of winning the ten yard dash and a 30 percent probability of winning the 50 yard dash. If the runner completes both events, what is the probability he wins exactly one of the races?

Question

kropot72 · Answer

Winning the ten yard dash and winning the fifty yard dash are independent events.
Let event A be winning the ten yard dash and not winning the fifty yard dash.
Let event B be winning the fifty yard dash and not winning the ten yard dash.
P(A) = 0.5 * (1 - 0.3) = 0.35
P(B) = 0.3 * (1 - 0.5) = 0.15
Events A and B are mutually exclusive. The probability of A or B is
$$P(A \cup B)=P(A)+P(B)=0.35+0.15$$