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Using the binomial distribution, there is a 0.6328 = 63.28% probability that she wins at most 1 prize.
For each box, there are only two possible outcomes, either it has a prize, or it does not. The probability of a box having a prize is independent of any other box, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- She buys 5 boxes, hence
- 1 in 4 boxes has a prize, hence
The probability is:
Hence:
Then
0.6328 = 63.28% probability that she wins at most 1 prize.
A similar problem is given at brainly.com/question/24863377