This is a binomial distribution problem. The binomial distribution model is appropriate for a sequence of n trials, or experiments, each of which yields a success with probability p and fails with probability 1 - p.

Here, n = 10 (the number of trials, which is the number of components in a box), p = 0.05 (the probability of success, which is the probability of a component being defective), and we want to find the probability that k = 1 (the number of successes, which is the number of defective components in a box).

The formula for the binomial probability is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where C(n, k) is the number of combinations of n items taken k at a time.

So, we can plug in the values:

P(X=1) = C(10, 1) * (0.05^1) * ((1-0.05)^(10-1))

= 10 * 0.05 * (0.95^9)

= 0.315

So, the probability that the box contains exactly 1 defective component is 0.315, which corresponds to option a.

Question

This is a binomial distribution problem. The binomial distribution model is appropriate for a sequence of n trials, or experiments, each of which yields a success with probability p and fails with probability 1 - p.

Here, n = 10 (the number of trials, which is the number of components in a box), p = 0.05 (the probability of success, which is the probability of a component being defective), and we want to find the probability that k = 1 (the number of successes, which is the number of defective components in a box).

The formula for the binomial probability is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where C(n, k) is the number of combinations of n items taken k at a time.

So, we can plug in the values:

P(X=1) = C(10, 1) * (0.05^1) * ((1-0.05)^(10-1))

= 10 * 0.05 * (0.95^9)

= 0.315

So, the probability that the box contains exactly 1 defective component is 0.315, which corresponds to option a.

Knowee AI · Accepted Answer

This is a binomial distribution problem. The binomial distribution model is appropriate for a sequence of n trials, or experiments, each of which yields a success with probability p and fails with probability 1 - p.

Here, n = 10 (the number of trials, which is the number of components in a box), p = 0.05 (the probability of success, which is the probability of a component being defective), and we want to find the probability that k = 1 (the number of successes, which is the number of defective components in a box).

The formula for the binomial probability is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where C(n, k) is the number of combinations of n items taken k at a time.

So, we can plug in the values:

P(X=1) = C(10, 1) * (0.05^1) * ((1-0.05)^(10-1))

= 10 * 0.05 * (0.95^9)

= 0.315

So, the probability that the box contains exactly 1 defective component is 0.315, which corresponds to option a.

A factory produces components of which 5% are defective. Components are packed in boxes of 10. A box is selected at random. What is the probability that the box contains exactly 1 defective component?Question 5Select one:a.0.315b.0.599c.0.401d.0.685

Question

Solution

Similar Questions

Upgrade your grade with Knowee