Question

A die is thrown 100 times. If getting an even number is considered as a success, then the
variance of the number of successes is
(a) 50
(b) 25
(c) 10
(d) 100
correct answer is (b)
can anyone show me the procedure???​

Answer 1

Answer:

(b) 25

Step-by-step explanation:

Let X be the number of successes.

As there are n=100 independent trials and probability p=3/6=1/2 of success on each trial, the random variable X has a binomial distribution

              X ∼ B(100, 1/2)

For a binomial distribution B(n, p), the expected value (mean) is np and the variance is npq = np(1-p).

So for X, the variance is

      var(X) = 100 × 1/2 × ( 1 - 1/2 )

               = 100 × 1/2 × 1/2

               = 25