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 are defective
(0.04)^3 = 0.04*0.04*0.04 = ?
To find the probability that all three alarm clocks are defective, we need to consider the probability of selecting a defective alarm clock for each of the three selections.
Given that the probability of selecting a defective alarm clock is 0.04, the probability of selecting a non-defective alarm clock (the complement of defective) in each selection would be 1 - 0.04 = 0.96.
Since each selection is independent (Charlie puts the clock back before selecting the next one), we can multiply the probabilities together to find the overall probability:
P(all three defective) = P(defective on 1st selection) * P(defective on 2nd selection) * P(defective on 3rd selection)
= 0.04 * 0.04 * 0.04
= 0.0016
Therefore, the probability that all three alarm clocks selected by Charlie are defective is 0.0016 or 0.16%.