A promotion on a cereal box says that 1 in 4 boxes will have a prize inside. What are the chances, to the nearest percent, of not opening a price in 5 boxes?

Question

You need to figure out what percent of a chance that you will not get a prize after purchasing 5 boxes

Answer 1

If one in four boxes has a prize in it, then every individual box has a 1/4 chance of having a prize in it. That also means that every box has a 3/4 chance of not having a prize in it.

 

If you open five boxes, each of them has a 3/4 chance of not having a prize in it. The chances that all five, in a row, don't have prizes are (3/4)×(3/4)×(3/4)×(3/4)×(3/4)=3⁵/4⁵=243/1024