Question

9. A fair cubical die is thrown four times. Use the binomial probability formula to calculate the probability of at least two 3's. (Marks: 4)

Answer 1

Answer:

Probability = 0.1319

Explanation:

Let the random variable, X = number of 3's in four rolls of a cubical die

When we want to calculate the probability of the number of success in a fixed number of trails (bernoull's trials i.e. two possible outcomes, success/failure), the binomial distribution follows.

Hence the sample size of 4 rolls will have a binomial distribution with parameters n and p.

n = number of trials = 4

p = probability of success in each roll = 1/6

The cumulative distribution function is defined as,

The required probability is,

(In excel use function =1-BINOM.DIST(1,4,1/6,TRUE))