Paper 1 · conditional probability
A head of school contacts parents by e-mail, letter or cellphone with probabilities 0.4, 0.1 and 0.5 respectively. The probability parents receive the message is 0.6 for e-mail, 0.8 for letter and 1 for cellphone, so the overall probability of receiving the message is 0.82. Given that the parents received the message, what is the probability that it was sent by e-mail?
A0.293
B0.240
C0.400
D0.600
Explanation: P(email|received) = P(email)xP(receive|email)/P(receive) = 0.24/0.82 = 12/41 = 0.293. (0.240 is the numerator alone, without dividing by P(receive); 0.400 is just the prior P(email); 0.600 is P(receive|email), not the required conditional probability.)
Derived from ZIMSEC Statistics Paper 1, November 2018, Q2
