Question

There are three social media groups on a mobile: Group I, Group II and Group III. The probabilities that Group I, Group II and Group III sending the messages on sports are 2/5, 1/2 and 2/3 respectively. The probability of opening the messages by Group I, Group II and Group III are 1/2, 1/4 and 1/4 respectively. Randomly one of the messages is opened and found a message on sports. What is the probability that the message was from Group III.

Answer 1

Let event A: Message sent on sports by group I,

event B: Message sent on sports by group II, 

event C: Message sent on sports by group III, 

event E: Message is opened. 

Given that the probabilities that Group I, 

Group II and Group III sending the messages on sports are 2/5, 1/2 and 2/3 respectively and the probability of opening the messages by Group I, Group II and Group III are 1/2, 1/4 and 1/4 respectively.

∴ P(A) = 2/5

P(B) = 1/2

P(C) = 2/3

P(E/A) = 1/2

P(E/B) = 1/4

P(E/C) = 1/4

Required probability = P(C/E)

By Baye’s theorem