The problem describes a geometric distribution. In a geometric distribution, we are interested in the number of failures before the first success.

Here, a "success" is defined as guessing correctly, and each guess is independent with a 1/5 = 0.2 probability of success.

The probability mass function of a geometric distribution is given by:

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

where:
- p is the probability of success
- k is the number of trials up to and including the first success

So, to find the probability that the first correct guess occurs on the 6th guess, we plug in p = 0.2 and k = 6:

P(X = 6) = (1 - 0.2)^(6 - 1) * 0.2
P(X = 6) = (0.8)^5 * 0.2
P(X = 6) = 0.32768

So, the probability that he doesn't guess correctly until his 6th guess is approximately 0.3277.

Question

The problem describes a geometric distribution. In a geometric distribution, we are interested in the number of failures before the first success.

Here, a "success" is defined as guessing correctly, and each guess is independent with a 1/5 = 0.2 probability of success.

The probability mass function of a geometric distribution is given by:

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

where:
- p is the probability of success
- k is the number of trials up to and including the first success

So, to find the probability that the first correct guess occurs on the 6th guess, we plug in p = 0.2 and k = 6:

P(X = 6) = (1 - 0.2)^(6 - 1) * 0.2
P(X = 6) = (0.8)^5 * 0.2
P(X = 6) = 0.32768

So, the probability that he doesn't guess correctly until his 6th guess is approximately 0.3277.

Knowee AI · Accepted Answer