Question

The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.

The probability that neither sound an alarm in the presence of smoke

Answer 1

Let the two events:

P(A )= The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke

P(B)= The probability that a smoke alarm will not function properly and sound an alarm in the presence of smoke

We are given

P(A) = 0.8

Therefore

P(B) = 1-0.8 = 0.2

Since the two events are independent, the probability that neither sound an alarm in the presence of smoke

P(B and B) = P(B) * P(B) = 0.2*0.2 = 0.04

Answer = 0.04