Final answer:
To find the probability that Jeff has to play the game exactly 5 times, we can use the concept of geometric probability. Each game Jeff plays is an independent event, and we can calculate the probability using the formula P(X = 5) = (1 - p)4 * p.
Step-by-step explanation:
To find the probability that Jeff has to play the game exactly 5 times, we can use the concept of geometric probability. In a geometric probability, the probability of success stays the same from trial to trial, which means each game Jeff plays is an independent event. Let's assume that the probability of winning the prize in one game is p.
The probability of Jeff winning the prize on his 5th game can be calculated as follows:
P(X = 5) = (1 - p)^4 * p
The exponent 4 represents the number of failures Jeff had before his fifth game, and the p represents the probability of success on the fifth game.Note that we need the value of p, the probability of winning the prize in one game, to calculate the exact probability of Jeff winning on his fifth game. Without that information, we cannot provide a numerical answer.