Correct Answer - Option 3 : 10
Concept:
Binomial distribution:
If a random variable X has binomial distribution as B (n, p) with n and p as parameters, then the probability of random variable is given as:
P( X = k) = nCk pk q(n - k) where q = p - 1, n is the number of observations, p is the probability of success & q is the probability of failure
Note: The mean of a binomial distribution is np and variance is npq.
Calculation:
Given: An unbiased die is thrown 72 times and getting a 4 on a throw is termed as success
As we know that when a die is thrown there are 6 outcomes.
Let the probability of getting 4 on a throw which is termed as success is denoted by p.
⇒ p = 1/6
Let the probability of failure is denoted by q = 1 - p.
⇒ q = 1 - 1/6 = 5/6
As we know that, variance of a binomial distribution = npq
\(\rm ⇒variance = 72 \times \frac{1}{6} \times \frac{5}{6}=10\)
Hence, the correct option is 3.
