Question

Aja's favorite cereal is running a promotion that says 1-in-4 boxes of the

cereal contain a prize. Suppose that Aja is going to buy 5 boxes of this
cereal, and let X represent the number of prizes she wins in these boxes.
Assume that these boxes represent a random sample, and assume that
prizes are independent between boxes.
What is the probability that she wins at most 1 prize in the 5 boxes?
You may round your answer to the nearest hundredth.
P(X ≤ 1) =

Answer 1

Explanation:

We can model the number of prizes Aja wins in 5 boxes of cereal as a binomial distribution with parameters n = 5 and p = 1/4, where n is the number of trials and p is the probability of success in each trial.

The probability of winning at most 1 prize can be calculated as follows:

P(X ≤ 1) = P(X = 0) + P(X = 1)

We can use the binomial probability formula to calculate each of these probabilities:

P(X = 0) = (5 choose 0) * (1/4)^0 * (3/4)^5 = 0.2373

P(X = 1) = (5 choose 1) * (1/4)^1 * (3/4)^4 = 0.3956

Therefore,

P(X ≤ 1) = 0.2373 + 0.3956 = 0.633

Rounding this answer to the nearest hundredth gives:

P(X ≤ 1) ≈ 0.63

So the probability that Aja wins at most 1 prize in the 5 boxes of cereal is approximately 0.63.