In a binomial experiment the probability of success is 0.05.What is the probability of two successes in seven trials?

A) 0.0036
B) 0.0000
C) 0.0406
D) 0.3667

Question

In a binomial experiment the probability of success is 0.05.What is the probability of two successes in seven trials?A)  0.0036B)  0.0000C)  0.0406D)  0.3667

Supreme Chidori · Accepted Answer

Final Answer : C, Explanation :  To find the probability of two successes in seven trials, we will use the binomial probability formula:P(X = k) = (n choose k) * p^k * (1-p)^(n-k)where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient (i.e. the number of ways to choose k items from a set of n items).In this case, we have n = 7 trials, k = 2 successes, and p = 0.05 probability of success. Plugging in these values, we get:P(X = 2) = (7 choose 2) * (0.05)^2 * (1-0.05)^(7-2)= 21 * 0.0025 * 0.8674= 0.0406Therefore, the best choice is C, with a probability of 0.0406.

In a binomial experiment the probability of success is 0.05.What is the probability of two successes in seven trials?

A) 0.0036
B) 0.0000
C) 0.0406
D) 0.3667

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