A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each
bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize
The probability that the customer must open 3 or more bottles before finding a prize is 0.64
Step-by-step explanation:
In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64