Question

A plane has four engines. Each engine has a probability of failing during flight of 0.3. What is the probability that no more than two engines fail during a flight? Assume the engines are independent.

Answer 1

To find the probability that no more than two engines fail during a flight, we can use the binomial distribution. The probability of a single engine failing is 0.3, so the probability of a single engine not failing is 0.7. We can calculate the probabilities of different combinations of engine failures and add them up to find the final probability.

Step-by-step explanation:

To find the probability that no more than two engines fail, we need to consider all the possible combinations of engine failures. There are four engines, and each engine can either fail or not fail during a flight.

We can use the binomial distribution to calculate the probabilities. The probability of a single engine failing is 0.3, so the probability of a single engine not failing is 1 - 0.3 = 0.7.

To find the probability that no engines fail, we calculate (0.7)^4 = 0.2401.

To find the probability that exactly one engine fails, we calculate 4C1 * (0.7)^3 * (0.3) = 0.4116.

Finally, to find the probability that exactly two engines fail, we calculate 4C2 * (0.7)^2 * (0.3)^2 = 0.2646.

The probability that no more than two engines fail is the sum of these probabilities: 0.2401 + 0.4116 + 0.2646 = 0.9163.