In a binomial experiment the probability of success is 0.06.What is the probability of two successes in seven trials?
A) 0.0036
B) 0.06
C) 0.0554
D) 0.28

Question

In a binomial experiment the probability of success is 0.06.What is the probability of two successes in seven trials?​
A) ​0.0036
B) ​0.06
C) ​0.0554
D) ​0.28

Quizplus · Accepted Answer

Using 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

P(X = 2) = (7 choose 2) * (0.06)^2 * (0.94)^5 
= (21) * (0.0036) * (0.735)^5 
= 0.05536

Therefore, the probability of two successes in seven trials is 0.0554 which is closest to option C (rounded to four decimal places).

In a Binomial Experiment the Probability of Success Is 0