Answer to Question #66704 in Statistics and Probability for Athira

Question

In a sequence of 4 trials with probability of success p=1/3,what is the probability that there will be exactly two successes?

Answer 1

We should use the Bernoulli formula:
P = Cn(k)*p^k*q^(n - k) = C4(2)*(1/3)^2*(2/3)^(4 - 2) = 4!/(2!*(4 - 2)!)*(1/3)^2*(2/3)^2 = 6*1/9*4/9 = 24/81 = 8/27