An apartment has two fire alarms. In the event of a fire, the probability that alarm A will fail is 0.004, and the probability that alarm B will fail is 0.01. Assume the two failures are independent, what is the probability that at least one alarm fails in the event of a fire

Answer: 0.0136

Step-by-step explanation:

Let events are:

A = alarm A will fail

B = alarm B will fail

We have given,

P (A) = 0.004, P (B) = 0.01

Since both events are independent, so

P (A and B) = P (A) x P (B)

= 0.04 x 0.01 = 0.0004

i. e. P (A and B) = 0.0004

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

= 0.004 + 0.01-0.0004=0.0136

Hence, the probability that at least one alarm fails in the event of a fire is 0.0136.