Answer:
a) P(b) = 0.147 or 14.7 %
b) P(i) = 0.77 or 77 %
c) P [ A ║ B ] = 0.6 or 60 %
Explanation:
a) The events Hector runs a marathon and finished within three hours is totally independent of probabilities of Whirlen
then probability of both of them finishing within three hours is
P(b) = Probability of Hector (finishing within 3 hours) * Probability of Whirlen (finishing within 3 hours )
P(b) = 0.42 * 0.35 ⇒ P(b) = 0.147 or P(b) = 14.7 %
b) The probability of at least one of them finishes within three hours is
P(i) = Probability of Hector (finishing within 3 hours) + Probability of Whirlen (finishing within 3 hours)
P(i) = 0.42 + 0.35 ⇒ P(i) = 0.77 or P(i) = 77 %
c) The probability of whirlen finishes within 3 hours given that Hector finished within three hours is express according to Bayes Theorem
Event A Hector finished within three hours : 0.42
Event B Whirlen finished within three hours : 0.35
Bayes Theorem:
P [ A ║ B ] = P(A) * P [ B ║ A ] / P(B)
P [ A ║ B ] = 0.42 * 0.50 / 0.35 ⇒ P [ A ║ B ] = 0.6