Three persons try to decode a secret message independently. Their probabilities of successfully decoding are 1/5, 1/4 and 1/3. What is the probability that the secret message will be revealed?
The question is asking what is P(at least one person decodes the message)Three persons try to decode a secret message independently. Their probabilities of successfully decoding are 1/5, 1/4 and 1/3. What is the probability that the secret message will be revealed?
This probability equals 1 - P(no one decodes the message)
No one decoding the message means that the first person didn't decode the message AND the second person didn't decode the message AND the thrid person didn't decode the message.
The probability that all three fail to decode the message is 4/5 x 3/4 x 2/3 = 2/5
So, P(at least one person decodes the message) = 1-2/5 = 3/5
