SOLUTION: The probability that Sam will win in a certain game whenever he plays is 2/5. If he plays two games, what is the probability that he will win just the first game?

Question 1077068: The probability that Sam will win in a certain game whenever he plays is 2/5. If he plays two games, what is the probability that he will win just the first game?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p = 2/5
q = 1 - 2/5 = 3/5

probability he wins any game he plays in is 2/5
probability he loses any game he plays in is 3/5

he plays 2 games.

probability he wins the first game only is 2/5 * 3/5 = 6/25

that's your solution.

probability he wins the second game only is 3/5 * 2/5 = 6/25

probability he wins both games is 2/5 * 2/5 = 4/25

probability he loses both games is 3/5 * 3/5 = 9/25

sum of all probabilities must be equal to 1.

6/25 + 6/25 + 4/25 + 9/25 = 25/25 = 1

everything checks out.

probability he wins the first game only is 6/25.

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