of the boxes of cruncho cereal on a supermarket shelf 25 percent contain a prize and the other 75 percent contain no prize. if Gerry buys two boxes of cruncho cereal which of the following is closest to the probability that neither box contain a prize??

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

Step-by-step explanation:

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

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

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