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?

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Q: 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?

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.

Steps: 10

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.