Question

chloe and jack play 4 games. the probability that chloe wins any game is 4/5. what is the probability that chloe wins for the 1st time in the 4th game?

Answer 1

$\dfrac{1}{5}\cdot\dfrac{1}{5}\cdot\dfrac{1}{5}\cdot\dfrac{4}{5}=\dfrac{4}{625}$

Answer 2

Probability of a Win:

P(Chloe Win) = 4/5

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Probability of a Lost:

P(Chloe Lost) = 1 - 4/5 = 1/5

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P(Chloe win first time in the 4th game) ⇒ She lost 3 games and win 4th game.

P(Chloe win first time in the 4th game) = 1/5 x 1/5 x 1/5 x 4/5 = 4/625

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Answer: 4/625