here is a keystone sample question: in a shipment of alarm clocks, the probability that one alarm clock is…

here is a keystone sample question: in a shipment of alarm clocks, the probability that one alarm clock is defective is 0.04. charlie selects three alarm clocks at random. if he puts each clock back with the rest of the shipment before selecting the next one, what is the probability that all three alarm clocks would be defective? 0.000064 0.00012 0.064 0.12

here is a keystone sample question: in a shipment of alarm clocks, the probability that one alarm clock is defective is 0.04. charlie selects three alarm clocks at random. if he puts each clock back with the rest of the shipment before selecting the next one, what is the probability that all three alarm clocks would be defective? 0.000064 0.00012 0.064 0.12

Answer

Explanation:

Step1: Identify probability of single - event

The probability that one alarm clock is defective, $p = 0.04$.

Step2: Use multiplication rule for independent events

Since the selections are made with replacement, the events are independent. The probability that all $n = 3$ alarm clocks are defective is $P=p\times p\times p=p^{3}$. Substitute $p = 0.04$ into the formula: $P=(0.04)^{3}=0.04\times0.04\times0.04 = 0.000064$.

Answer:

A. 0.000064