Question

N=15, p=0.35,x=2 p(2)=

Answer 1

To find p(2) in a binomial distribution, use the formula p(x) = C(n, x) * p^x * (1-p)^(n-x), where n is the total number of trials, x is the number of successful trials, and p is the probability of success. Plugging in the given values, we find that p(2) is approximately 0.203.

Step-by-step explanation:

To find p(2), we use the formula for the probability mass function of a binomial distribution:

`p(x) = C(n, x) * p^x * (1-p)^(^n^-^x^),`

where C(n, x) represents the number of combinations of n items taken x at a time, n represents the total number of trials, x represents the number of successful trials, and p represents the probability of success in each trial.

In this case, we have n = 15, p = 0.35, and x = 2. Plugging these values into the formula, we get

`p(2) = C(15, 2) * 0.35^2 * (1-0.35)^(^1^5^-^2^).`

Simplifying further, we have

`p(2) = 105 * 0.35^2 * 0.65^1^3.`

Evaluating this expression, we find that p(2) is approximately 0.203.

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