A grocery manager discovered that on any given weekday 55 of

A grocery manager discovered that, on any given weekday, 55% of the customer sales amount to more than $100. What is the probability that none of the first 3 sales will be more than $100? Treat the sales as independent events

Solution

55% of customer sales amount to more than 100 dollars.

i.e. P(Sales >100 $) = 0.55

Let X be the sales >100

Then X is independent of each day and there are two outcomes either >100 or <100

Hence X is binomial with p = 0.55 and n = 3

Required probability = probability that none of the first 3 sales will be more than $100

= P(x=0 in 3 trials)

= (1-0.55) (1-0.55)(1-0.55) since each trial is independent.

= 0.091125