x is a binomial random variable. (Give your answers correct to three decimal places.)

(e) Calculate the probability of x for: n = 3, x = 1, p = 0.45
P(x) = .I got 0.41

(f) Calculate the probability of x for: n = 6, x = 6, p = 0.25
P(x) = I got 1.50

(E) Yes it is correct but remembered that your answer should be three decimal places.

0.408

(F) = 0.000244

To calculate the probability of x for a binomial random variable, you can use the probability mass function (PMF) formula:

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

where n is the number of trials, x is the number of successful outcomes, p is the probability of success in a single trial, and nCx represents the number of combinations of n items taken x at a time.

Let's calculate the probabilities for the given scenarios:

(e) n = 3, x = 1, p = 0.45

Using the PMF formula:
P(x) = 3C1 * 0.45^1 * (1-0.45)^(3-1)
= 3 * 0.45 * 0.55^2
= 0.298

Therefore, the probability of x = 1 for the given parameters is 0.298 (correct to three decimal places).

(f) n = 6, x = 6, p = 0.25

Using the PMF formula:
P(x) = 6C6 * 0.25^6 * (1-0.25)^(6-6)
= 1 * 0.25^6 * 0.75^0
= 0.25^6 * 1
= 0.000244

Therefore, the probability of x = 6 for the given parameters is 0.000244 (correct to three decimal places).

Note: It is important to note that probabilities cannot exceed 1, so we cannot have a probability of 1.50.