At a gas station, suppose that 45% of the customers purchase premium grade gas. Assume that these customers decide independently. Find the probability that at least one of the next three customers purchases premium gas. (Hint: Think about the complement.)

The answer to the question is

The probability that at least one of the next three customers purchases premium gas is the complement of the probability that none of the next three customers purchase premium gas = 1 - (1-P(A))³ = 0.834

Step-by-step explanation:

The probability that a customer would purchase premium grade = 45 %

That is P(A) = 0.45 and

The probability that the customer would purchase another  grade = P(B) = 0.55

Therefore the probability of at least one of the next three customers purchase premium gas is

P(k=0) = (1 - P)ⁿ and the probability of at least one customer purchases premium gas is the compliment of the probability that the next three customers purchase another gas brand

that is (1 - P(A))×(1 - P(A))×(1 - P(A)) = P(B)×P(B)×P(B) = 0.55³  and the complement is 1 - 0.55³  = 0.834

expression #3 is not equivalent. the others are.

i dont know if you cant find a way its best to actually add all of them start from 105 tho

step-by-step explanation: