Question

The Air Force receives 20% of its parachutes from Company C1, 55% from company C2, and the rest from company C3. The probability that a randomly selected parachute fails to open is 0.0025, 0.002, and 0.0022 depending on whether it came from Company C1, C2, or C3 respectively. If a randomly selected parachute fails to open, what is the probability that it came from Company C3?

a .00055
b .00215
c .0022
d .250
e .256

Answer 1

To determine the probability that a failed parachute came from Company C3, we used Bayes' theorem, which involves the failure probabilities and the percentage of parachutes supplied by each company. After summing the products of these probabilities,

The correct option is d. 0.250.

Step-by-step explanation:

The problem we are solving is a classic example of Bayes' theorem, which provides a way to update the probability estimate for a hypothesis as additional evidence is acquired. To find the probability that a parachute which fails to open came from Company C3, we'll use the given failure rates and the proportion of parachutes from each company.

First, we calculate the total probability of a parachute failing to open by summing the products of the parachutes' individual failure probabilities and their percentages:

P(Failure) = (P(C1) × P(Failure|C1)) + (P(C2) × P(Failure|C2)) + (P(C3) × P(Failure|C3))

P(Failure) = (0.20 × 0.0025) + (0.55 × 0.002) + (0.25 × 0.0022)

Then, we calculate the probability that a parachute that failed came from Company C3 using Bayes' theorem:

P(C3|Failure) = (P(C3) × P(Failure|C3)) / P(Failure)

After calculating the individual probabilities and sum, we can solve for P(C3|Failure).

The correct answer to the student's question is (d) 0.250, as this represents the conditional probability of a parachute coming from Company C3 given that it fails to open.