Question

3. Past records indicate that the probability of online retail orders that turn ut to be fraudulent is 0.08. Suppose that, on a given day, 8 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable. a. What is the probability that less than two online retail orders will turn out to be fraudulent?

Answer 1

A binomial distribution can be understood as the probability of a trail with two and only two outcomes. It is a type of distribution that has two different outcomes namely, ‘success’ and ‘failure’.

It is derived from the formula: nCx*P^x*(1-P)^n-x

x is the total number of successes.
p is chances of a success on an individual experiment.
n is the number of trials

x: Since it asks for probability for less than 2, this is 1

p: 0.08

n: 8

Therefore substituting the above details in the formula:

8!/(1! x 7!) x (0.08)^1 x (1 - 0.08)^(8-1) = 0.357022