you are going to play two games the probability you win the first game is 0.60 if you win the first game the probability you will win the second game is 0.75 if you lose the first game the probability you win the second game is 0.55. what is the probability you win exactly one game
just list the cases:
P(WL) = 0.60*0.25
P(LW) = 0.40*0.55
Since they are mutually exclusive,
P(WL)+P(LW) = 0.37
To find the probability of winning exactly one game, we need to consider two cases:
Case 1: Winning the first game and losing the second game.
The probability of winning the first game is 0.60, and the probability of losing the second game is 0.25 (1 - 0.75). So the probability of winning the first game and losing the second game is 0.60 * 0.25 = 0.15.
Case 2: Losing the first game and winning the second game.
The probability of losing the first game is 1 - 0.60 = 0.40, and the probability of winning the second game is 0.55. So the probability of losing the first game and winning the second game is 0.40 * 0.55 = 0.22.
To find the overall probability of winning exactly one game, we need to sum the probabilities from both cases:
Overall probability = Probability of winning first game and losing second game + Probability of losing first game and winning second game
Overall probability = 0.15 + 0.22
Overall probability = 0.37
Therefore, the probability of winning exactly one game is 0.37 or 37%.
To find the probability of winning exactly one game, we need to consider two possibilities: winning the first game and losing the second game, or losing the first game and winning the second game.
Let's calculate the probability of each scenario:
1. Probability of winning the first game and losing the second game:
- Probability of winning the first game: 0.60
- Probability of losing the second game: 1 - Probability of winning the second game if you win the first game (1 - 0.75)
- Probability of winning both games: Probability of winning the first game * Probability of losing the second game
- Probability of winning the first game and losing the second game: 0.60 * (1 - 0.75) = 0.60 * 0.25 = 0.15
2. Probability of losing the first game and winning the second game:
- Probability of losing the first game: 1 - Probability of winning the first game (1 - 0.60)
- Probability of winning the second game: Probability of winning the second game if you lose the first game (0.55)
- Probability of winning both games: Probability of losing the first game * Probability of winning the second game
- Probability of losing the first game and winning the second game: (1 - 0.60) * 0.55 = 0.40 * 0.55 = 0.22
Now, we can add up the probabilities of winning exactly one game:
Probability of winning exactly one game = Probability of winning the first game and losing the second game + Probability of losing the first game and winning the second game
Probability of winning exactly one game = 0.15 + 0.22 = 0.37
Therefore, the probability of winning exactly one game is 0.37, or 37%.