a PX 4SolutionX No of successes in 5 independent trials X

a. P(X = 4)

Solution

X = No of successes in 5 independent trials

X is binomial (5, 2/5)

a) P(X=4) = 5C4 (2/5)⁴(3/5)

=0.0768

b) P(2<=x<=4)

= P(2)+P(3)+P(4)

=5C2 (2/5)²(3/5)³+5C3 (2/5)³(3/5)²+ 5C4 (2/5)⁴(3/5)

=0.3456+0.2304+ 0.0768

= 0.6528

=