Question

A smoke-detector system uses two devices, A and B. If smoke is present, the probability that it will be detected by device A is 0.93; by device B, 0.98; and by both devices, 0.92. a. If smoke is present, what is the probability that it will be detected by either device A or device B?

Answer 1

To find the probability that smoke will be detected by either device A or B, we can calculate the probability of the union of these events using the formula P(A or B) = P(A) + P(B) - P(A and B). Plugging in the given values, the probability is 0.99, or 99%.

Step-by-step explanation:

To find the probability that smoke will be detected by either device A or device B, we need to calculate the probability of the union of these events. We can use the formula:

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

Plugging in the given values:

P(A or B) = 0.93 + 0.98 - 0.92 = 0.99

The probability that smoke will be detected by either device A or device B is 0.99, or 99%.