Assume an office has two telephones (A and B) with separate lines and different telephone numbers. The probability that telephone A rings when the office is closed is .30. The probability that telephone B rings when the office is closed is .20

What is the probability that neither telephone rings when the office is closed

That neither ring

Probability that A does not ring is .7

Probability that B does not ring is .8

Multiply the two.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

To find the probability that neither telephone rings when the office is closed, we first need to find the probability that each telephone does ring when the office is closed.

Given that the probability that telephone A rings when the office is closed is 0.30, the probability that telephone A does not ring (let's call it event A') is 1 - 0.30 = 0.70.

Similarly, given that the probability that telephone B rings when the office is closed is 0.20, the probability that telephone B does not ring (let's call it event B') is 1 - 0.20 = 0.80.

Since the events of telephone A not ringing (A') and telephone B not ringing (B') are independent events (one telephone ringing or not ringing does not affect the other), we can find the probability that neither telephone rings by multiplying the probabilities of each individual telephone not ringing:

P(neither telephone rings) = P(A' and B') = P(A') * P(B') = 0.70 * 0.80 = 0.56

Therefore, the probability that neither telephone rings when the office is closed is 0.56 or 56%.