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In a game, the probability of winning is 0.25. If a player plays 4 times, what i

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Question: 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?

Options:

  1. 0.75
  2. 0.84
  3. 0.93
  4. 0.99

Correct Answer: 0.84

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.

In a game, the probability of winning is 0.25. If a player plays 4 times, what i

Practice Questions

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?
  1. 0.75
  2. 0.84
  3. 0.93
  4. 0.99

Questions & Step-by-Step Solutions

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?
  • 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.
  • Probability of Independent Events – Understanding how to calculate the probability of independent events occurring, specifically using complementary probabilities.
  • Complementary Probability – Using the concept of complementary probability to find the likelihood of at least one success in multiple trials.
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