In a lottery, the probability of winning is 0.05. If a person buys 10 tickets, w

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Question: 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?

Options:

Correct Answer: 0.5

Solution:

P(winning at least once) = 1 - P(not winning) = 1 - (0.95^10) ≈ 0.4013.

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?

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?

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.

Probability of Independent Events – The question tests the understanding of calculating the probability of at least one success in independent trials using the complement rule.
Complement Rule – It assesses the ability to apply the complement rule, which states that the probability of at least one event occurring is one minus the probability of the event not occurring.