Question

If the probability that a fluorescent light has a useful life of at least 800 hours is 0.9 , find the probabilities that among 20 such lights (a) exactly 18 will have a useful life of at least 800 hours; (b) at least 15 will have a useful life of at least 800 hours; (c) at least 2 will not have a useful life of at least 800 hours.

Answer 1

To find the probabilities in this scenario, use the binomial probability formula. Calculate P(18), calculate P(15 or more), and calculate P(at least 2) using the given formula.

Step-by-step explanation:

To find the probabilities in this scenario, we can use the binomial probability formula. The formula is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

Where:

P(x) is the probability of getting exactly x successes,

n is the number of trials,

p is the probability of success on a single trial,

x is the number of successes desired.

Let's calculate the probabilities:

(a) To find the probability that exactly 18 lights will have a useful life of at least 800 hours:

P(18) = (20C18) * 0.9^18 * (1-0.9)^(20-18)

(b) To find the probability that at least 15 lights will have a useful life of at least 800 hours:

P(15 or more) = P(15) + P(16) + ... + P(20)

P(15 or more) = P(15) + P(16) + P(17) + P(18) + P(19) + P(20)

(c) To find the probability that at least 2 lights will not have a useful life of at least 800 hours:

P(at least 2) = 1 - P(0) - P(1)