Question

Exercise 15. Lin and Mark each attempt independently to decode a message. If the prob- ability that Lin will decode the message is 0.80 and the probability that Mark will decode the message is 0.70, find the probability that (a) both will decode the message (b) at least one of them will decode the message (c) neither of them will decode the message

Answer 1

Let A: Lin will decode the message

B: Mark will decode the message.

P(A)= 0.80 and P(B) = 0.70

Since events A and B are given to be independent it means that

P(A and B) = P(A). P(B)

and P( A or B )=P(A) + P(B) - P( A and B)

a.) P( both will decode the message)= P( A and B ) = 0.80×0.70= 0.56

b.) P(at least one of them will decode the message) = P( A or B )

= 0.80 + 0.70 - 0.56 = 0.94

c.) P( neither of them will decode the message) = 1 - P( A or B) = 1 - 0.94 = 0.06