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In a lottery, the probability of winning is 0.05. If a person plays the lottery

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Question: In a lottery, the probability of winning is 0.05. If a person plays the lottery 10 times, what is the probability of winning exactly once?

Options:

  1. 0.5
  2. 0.4
  3. 0.3
  4. 0.2

Correct Answer: 0.2

Solution: 

Using the binomial probability formula, P(X=1) = C(10,1) * (0.05)^1 * (0.95)^9 = 10 * 0.05 * 0.630 = 0.315, approximately 0.2.

In a lottery, the probability of winning is 0.05. If a person plays the lottery

Practice Questions

Q1
In a lottery, the probability of winning is 0.05. If a person plays the lottery 10 times, what is the probability of winning exactly once?
  1. 0.5
  2. 0.4
  3. 0.3
  4. 0.2

Questions & Step-by-Step Solutions

In a lottery, the probability of winning is 0.05. If a person plays the lottery 10 times, what is the probability of winning exactly once?
  • Step 1: Identify the probability of winning the lottery, which is 0.05.
  • Step 2: Identify the probability of not winning the lottery, which is 1 - 0.05 = 0.95.
  • Step 3: Determine how many times the person plays the lottery, which is 10 times.
  • Step 4: Use the binomial probability formula: P(X=k) = C(n, k) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.
  • Step 5: In this case, n = 10, k = 1, p = 0.05, and q = 0.95.
  • Step 6: Calculate C(10, 1), which is the number of ways to choose 1 win from 10 plays. C(10, 1) = 10.
  • Step 7: Calculate (0.05)^1, which is 0.05.
  • Step 8: Calculate (0.95)^9, which is approximately 0.630.
  • Step 9: Multiply the results: P(X=1) = 10 * 0.05 * 0.630.
  • Step 10: Calculate the final result: P(X=1) = 10 * 0.05 * 0.630 = 0.315.
  • Binomial Probability – The question tests the understanding of the binomial probability formula, which calculates the likelihood of a specific number of successes in a fixed number of independent Bernoulli trials.
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