A control tower at an airport has two antennas for sending radio signals to appr

Question

A control tower at an airport has two antennas for sending radio signals to approaching planes. Each message is sent from the tower, (T), to antenna A, (A), and from the tower to antenna B, (B). The probabilities for these messages to get to the antennas are as follows:

P(TA) = 0.90 P(TB) = 0.75

These probabilities are not independent, however:

P(TB | TA) = 0.80

If the signals reach the antennas, they are sent to the plane, (P).

The probabilities of the signals getting from the antennas to the plane are as follows:

P(AP) = 0.60 P(BP) = 0.70

Note: the above two probabilities are independent of other outcomes.

Find the probability that one or more messages get to the plane.

Explanation / Answer

Find the probability that one or more messages get to the plane.

P( one or more messages get to the plane ) = 0.60 + 0.70 - 0.90*0.75 = 0.625

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