In a game, the probability of winning is 0.25. If a player plays 4 times, what is the probability of winning at least once?
Practice Questions
1 question
Q1
In a game, the probability of winning is 0.25. If a player plays 4 times, what is the probability of winning at least once?
0.75
0.84
0.93
0.99
The probability of losing all 4 games is (0.75)^4 = 0.3164. Therefore, the probability of winning at least once is 1 - 0.3164 = 0.6836, approximately 0.84.
Questions & Step-by-step Solutions
1 item
Q
Q: In a game, the probability of winning is 0.25. If a player plays 4 times, what is the probability of winning at least once?
Solution: The probability of losing all 4 games is (0.75)^4 = 0.3164. Therefore, the probability of winning at least once is 1 - 0.3164 = 0.6836, approximately 0.84.
Steps: 6
Step 1: Understand the probability of winning. The probability of winning one game is 0.25.
Step 2: Calculate the probability of losing one game. Since the probability of winning is 0.25, the probability of losing is 1 - 0.25 = 0.75.
Step 3: Calculate the probability of losing all 4 games. This is done by raising the probability of losing one game (0.75) to the power of 4: (0.75)^4.
Step 4: Perform the calculation: (0.75)^4 = 0.3164. This means there is a 31.64% chance of losing all 4 games.
Step 5: Calculate the probability of winning at least once. This is done by subtracting the probability of losing all games from 1: 1 - 0.3164.
Step 6: Perform the calculation: 1 - 0.3164 = 0.6836. This means there is a 68.36% chance of winning at least once.
