Question

In a store 25% of the boxes of cereal contain a prize. 75% of the cereal contains no prize. if you buy two boxes of cereal, what is the probability that neither box contains a prize.

Answer 1

The probability that neither box contains a prize is 0.5625 or 56.25%

Explanation:

Independent Events

It's referred as to the case when the probability of success (or failure) of the event A doesn't interfere with the probability of B. In this question we'll assume there are enough boxes of cereal of each type to make the choosing of one of them affect very little the choosing of the other one.

Let's call p=0.25 to the probability of getting a cereal box with a prize, and q=0.75 to the negation of p, i.e. the probability of getting a ceral box without a prize. There are four possible combinations: {pp,pq,qp,qq}. We need to find the probability of the combination qq. We compute it as the product of the individual probabilities

`P(qq)=q\cdot q=q^2=0.75^2=0.5625`

In other words, the probability that neither box contains a prize is 0.5625 or 56.25%