Question

A binomial probability experiment is conducted with the given

parameters. Compute the probability of x successes in the n
independent trials of the experiment.
n​=12, p​=0.6, x=7
p(7)=_____

Answer 1

The probability of 7 successes in 12 independent trials with a success probability of 0.6 is approximately 0.9231.

Step-by-step explanation:

To compute the probability of x successes in a binomial probability experiment, you can use the formula P(x) = (nCx) * (p^x) * (q^(n-x)), where n is the number of trials, p is the probability of success, q is the probability of failure (1-p), and nCx represents the number of combinations of n items taken x at a time. In this case, n = 12, p = 0.6, and x = 7. Therefore, the probability of 7 successes is:

P(7) = (12C7) * (0.6^7) * (0.4^5)

Let's calculate:

P(7) = (12! / (7! * (12-7)!)) * (0.6^7) * (0.4^5)

P(7) ≈ 792 * 0.1176 * 0.01024

P(7) ≈ 0.9231