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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. P(X > 3), n = 5, p = 0.2

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Answer:

0.0064

0.00032

Step-by-step explanation:

Given the details:

P(X > 3), n = 5, p = 0.2

The binomial distribution is related using the formula:

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

q = 1 - p = 1 - 0.2 = 0.8

P(X > 3) = p(x = 4) + p(x = 5)

P(x = 4) = 5C4 * 0.2^4 * 0.8^1 = 5 * 0.2^4 * 0.8^1 = 0.0064

P(x = 5) = 5C5 * 0.2^5 * 0.8^0 = 1 * 0.2^5 * 0.8^0 = 0.00032

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