Henry is a quality control inspector. He is watching the production line for Barb's Raisin Cookie. Henry will reject a cookie with less than 8 raisins. In the past, one out of every 100 cookies had less than 8 raisins. Find the probability that the first cookie Henry rejects is the 5th cookie on the line.

Raymond has exactly 360 square inches of cardboard to make a box.he wants two of the dimensions to be 6 inches and the other one to be a whole number of inches.how many different size boxes can he make?

To find the probability that the first cookie Henry rejects is the 5th cookie on the line, we need to understand that this situation follows a geometric distribution. The geometric distribution models the number of Bernoulli trials (in this case, inspecting cookies) until the first success (in this case, rejecting a cookie).

In this scenario, the probability of rejecting a cookie with less than 8 raisins is given as 1 out of every 100 cookies, or p = 1/100. Since the probability of success (rejecting a cookie) remains the same for each cookie, it follows a Bernoulli distribution.

The formula for the geometric distribution is as follows:

P(X = k) = (1 - p)^(k-1) * p

Where:
- P(X = k) is the probability of the first success (rejecting a cookie) occurring on the kth trial.
- (1 - p) is the probability of failure on each trial before the first success.
- k is the number of trials until the first success.
- p is the probability of success on each trial.

In our case, we want to find the probability that the first cookie Henry rejects is the 5th cookie on the line, so k = 5. Substituting the values into the formula, we get:

P(X = 5) = (1 - 1/100)^(5-1) * (1/100)

Simplifying further:

P(X = 5) = (99/100)^4 * (1/100)

P(X = 5) ≈ 0.96059601 * 0.01

P(X = 5) ≈ 0.00960596

Therefore, the probability that the first cookie Henry rejects is the 5th cookie on the line is approximately 0.00960596, or about 0.96%.