Question

A data transmission channel malfunctions with probability 0.10, but it has a backup channel which malfunctions with probability 0.15. The system works as long as either the main channel or the backup channel functions properly. If the probability that both function properly is 0.80, what is the probability that the system functions?

Answer 1

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Let A and B be events that either main or backup works

for the system to function either A should work or B should work,

lets represent the same in terms of probability set values, as following:

P(system functions) = P( A or B works) = P(A) + P(B) - P(A and B) = (1-.1) + (1-.15) - .80 = 0.9+0.85-0.80

= 0.95

the probability that the system functions is 0.95