In a lottery, the probability of winning is 0.05. If a person buys 10 tickets, what is the probability of winning at least once?
Practice Questions
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Q1
In a lottery, the probability of winning is 0.05. If a person buys 10 tickets, what is the probability of winning at least once?
0.5
0.4
0.6
0.3
P(winning at least once) = 1 - P(not winning) = 1 - (0.95^10) ≈ 0.4013.
Questions & Step-by-step Solutions
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Q
Q: In a lottery, the probability of winning is 0.05. If a person buys 10 tickets, what is the probability of winning at least once?
Solution: P(winning at least once) = 1 - P(not winning) = 1 - (0.95^10) ≈ 0.4013.
Steps: 6
Step 1: Understand the probability of winning a single ticket, which is 0.05.
Step 2: Calculate the probability of not winning with a single ticket. This is 1 - 0.05 = 0.95.
Step 3: Since the person buys 10 tickets, calculate the probability of not winning with all 10 tickets. This is 0.95 raised to the power of 10, which is 0.95^10.
Step 4: Use a calculator to find 0.95^10, which is approximately 0.5987.
Step 5: Now, to find the probability of winning at least once, subtract the probability of not winning from 1. This is 1 - 0.5987.
Step 6: Calculate 1 - 0.5987, which is approximately 0.4013.
