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In a certain game, the probability of winning is 0.3. If a player plays the game

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Question: 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?

Options:

  1. 0.163
  2. 0.836
  3. 0.5
  4. 0.7

Correct Answer: 0.836

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.

In a certain game, the probability of winning is 0.3. If a player plays the game

Practice Questions

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?
  1. 0.163
  2. 0.836
  3. 0.5
  4. 0.7

Questions & Step-by-Step Solutions

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?
  • 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.
  • Probability of Independent Events – Understanding how to calculate the probability of independent events occurring, specifically using the complement rule.
  • Complement Rule – Using the complement of an event to find the probability of at least one success in multiple trials.
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