Math  /  Data & Statistics

QuestionA fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner.
If Jeff keeps playing until he wins a prize, what is the probability that he has to play the game exactly 5 times? (0.75)5(0.75)^{5} (0.25)5(0.25)^{5} (0.75)4(0.75)^{4} (51)(0.75)4(0.25)\binom{5}{1}(0.75)^{4}(0.25) (0.75)4(0.25)(0.75)^{4}(0.25)

Studdy Solution
Identify the correct probability expression: - The probability of losing a game is 0.75 0.75 . - The probability of winning a game is 0.25 0.25 . - Jeff must lose the first 4 games and win the 5th game.
The expression for this scenario is:
(0.75)4×0.25 (0.75)^4 \times 0.25
The correct probability that Jeff has to play the game exactly 5 times is:
(0.75)4×0.25 \boxed{(0.75)^4 \times 0.25}

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