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?
prob all three defective
= (.04)^3 = .000064
My question to you:
What would it be if he had not returned the clocks after checking them?
im not sure
To find the probability that all three alarm clocks are defective, we need to multiply the probabilities of each event happening.
Given that the probability that one alarm clock is defective is 0.04, the probability that one alarm clock is not defective is 1 - 0.04 = 0.96.
Since Charlie selects the alarm clocks one at a time and puts them back before selecting the next one, the probability of selecting a defective alarm clock each time remains the same.
Therefore, the probability that all three alarm clocks are defective can be calculated as follows:
P(all three alarm clocks are defective) = P(defective) * P(defective) * P(defective)
P(all three alarm clocks are defective) = 0.04 * 0.04 * 0.04
P(all three alarm clocks are defective) = 0.000064 or 0.0064%
To find the probability that all three alarm clocks are defective, we need to multiply together the individual probabilities of selecting a defective alarm clock each time.
Given that the probability of selecting a defective alarm clock is 0.04, the probability of selecting a non-defective alarm clock is 1 - 0.04 = 0.96 (complement rule).
Since Charlie is putting each clock back with the rest of the shipment before selecting the next one, the probability of selecting a defective alarm clock remains the same for each selection.
Therefore, the probability of selecting three defective alarm clocks in a row is:
P(all three defective) = P(defective) * P(defective) * P(defective)
= 0.04 * 0.04 * 0.04
= 0.000064
So, the probability that all three alarm clocks are defective is 0.000064 or 0.0064%.