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A breakfast cereal company is running a competition: 2 in every 8 cereal boxes contain a prize. Emily bought a box of their rice pops and a box of their corn flakes. What is the probability that she won at least 1 prize?

We need to know the probability of Emily winning 1 or 2 prizes. An easy way to do this is to calculate the probability of her not winning a prize and subtracting this amount from 1.

The probability of not winning a prize in the rice pops box is 6/8 (6 in every 8 boxes do not contain a prize). The probability of her not winning a prize in the corn flakes box is also 6/8. To find the probability of both boxes not containing a prize we multiply these two figures.

6/8 x 6/8 = 36/64 = 9/16

Therefore, the probability of Emily not winning a prize is 9/16.

To find the probability of Emily winning one or more prizes, we subtract 9/16 from 1.

1 - 9/16 = 7/16.

So, the probability that Emily won at least one prize is 7/16.

Here is another way to solve this problem...

What are all the possible ways that Emily could have won 1 or 2 prizes?

1) The rice pops box contained a prize and the corn flakes box contained a prize. The probability of this occurring is 2/8 x 2/8 = 1/16

2) The rice pops box contained a prize and the corn flakes box did not contain a prize. The probability of this occurring is 2/8 x 6/8 = 3/16

3) The rice pops box did not contain a prize and the corn flakes box contained a prize. The probability of this occurring is 6/8 x 2/8 = 3/16

Now we must add all of these probabilities together to find the probability of Emily winning one or two prizes.

1/16 + 3/16 + 3/16 = 7/16

As we found above, the probability of her winning at least one prize is 7/16.

Here is some more information on probability.