In a certain game, the probability of winning is 0.3. If a player plays the game 5 times, what is the probability of winning at least once?
Practice Questions
1 question
Q1
In a certain game, the probability of winning is 0.3. If a player plays the game 5 times, what is the probability of winning at least once?
0.163
0.836
0.5
0.7
The probability of losing all 5 games is (1 - 0.3)^5 = 0.168. Therefore, the probability of winning at least once is 1 - 0.168 = 0.832, which rounds to 0.836.
Questions & Step-by-step Solutions
1 item
Q
Q: In a certain game, the probability of winning is 0.3. If a player plays the game 5 times, what is the probability of winning at least once?
Solution: The probability of losing all 5 games is (1 - 0.3)^5 = 0.168. Therefore, the probability of winning at least once is 1 - 0.168 = 0.832, which rounds to 0.836.
Steps: 6
Step 1: Understand the probability of winning the game, which is given as 0.3.
Step 2: Calculate the probability of losing the game. This is done by subtracting the winning probability from 1: 1 - 0.3 = 0.7.
Step 3: Since the player plays the game 5 times, we need to find the probability of losing all 5 games. This is calculated as (0.7)^5.
Step 4: Calculate (0.7)^5. This equals 0.16807 (approximately 0.168).
Step 5: Now, to find the probability of winning at least once, subtract the probability of losing all games from 1: 1 - 0.168 = 0.832.
Step 6: The final answer is the probability of winning at least once, which is approximately 0.832.
