In order to attract customers, an ice cream company has started a STAR game. Any person who collects four stars gets a free family size bucket of ice cream. Suppose that the probability of an ice cream pack contains a star is 0.3 (an ice cream pack cannot contain more than one star). Bob, ( a neighborhood child) has 1 star already. Find the probability that Bob has to buy 5 more ice cream packs to win the prize.

To find the probability that Bob has to buy 5 more ice cream packs to win the prize, we need to calculate the probability of not getting a star in each ice cream pack.

Given that the probability of getting a star in an ice cream pack is 0.3, the probability of not getting a star is 1 - 0.3 = 0.7.

Since Bob already has 1 star, he needs to collect 3 more stars to win the prize. Based on the information given, we can assume that each ice cream pack is independent, meaning that the probability of getting a star is the same for each pack.

To find the probability of not getting a star in 5 packs, we need to multiply the probabilities together since they are independent events.

P(Not getting a star in one pack) = 0.7
P(Not getting a star in 5 packs) = (0.7)^5

Therefore, the probability that Bob has to buy 5 more ice cream packs to win the prize is (0.7)^5 = 0.16807, or approximately 16.81%.