Alan's Exciting Soda Game Strategy!

What strategy did Alan use for the 1-in-6 wins game?

Find the probability that he buys exactly 5 bottles and the probability that he buys no more than 8 bottles.

Answer:

a) The probability of buying exactly 5 bottles would be: P(X = 5) = 0.06691

b) The probability of buying bottles not more than 8 would be: P(X ≤ 8) = 0.791784

Alan decided to use a different strategy for the 1-in-6 wins game by purchasing one 20-ounce bottle of soda at a time until he gets a winning bottle. This strategy keeps the excitement alive as he continues to try his luck with each purchase.

a) Given that the winning probability is 1/6, the probability of buying exactly 5 bottles with percentile X = 5 can be calculated using the geometric distribution formula: P(X = 5) = 0.06691. This means that there is a 6.691% chance that Alan will buy exactly 5 bottles before winning.

b) Similarly, the probability of buying bottles not more than 8 can be calculated using the geometric distribution formula as well. With a winning probability of 1/6, the probability of buying no more than 8 bottles (P(X ≤ 8) = 0.791784) shows that Alan has a 79.1784% chance of winning within the first 8 bottles.

By utilizing this strategic approach, Alan adds an element of anticipation and thrill to the game, making each purchase a thrilling experience. The probabilities calculated demonstrate the likelihood of Alan's success with his new soda game strategy.

For more information on probability calculations and geometric distribution, you can explore further resources to enhance your understanding of this exciting mathematical concept!