Let X B (6, 1 2 ) . Then the maximum probability occurs at

Step-by-step solution

Given X B (6, 1 2 ) , the probability mass function is given by P(X = x) = ⁶C_ x ( 1 2 )^ x (1 - 1 2 )^ 6-x = ⁶C_ x ( 1 2 )⁶ To maximize P(X = x) , the binomial coefficient ⁶C_ x must be maximum. For an even integer n , the maximum value of ^ n C_ x occurs at x = n 2 . Here n = 6 , so the maximum value occurs at x = 6 2 = 3 . Thus, the maximum probability occurs at X = 3 .