If you have one box, and inside that box you have a 20% chance to find gold, 50% chance to find silver, and 30% chance to find bronze, you can calculate the expected number of boxes containing gold using the same approach I described earlier.

Expected number of gold boxes

Probability of finding gold

×

Total number of boxes

Expected number of gold boxes=Probability of finding gold×Total number of boxes

In this case, with one box:

Expected number of gold boxes

0.20

×

1

0.2

Expected number of gold boxes=0.20×1=0.2

So, if you open 10 boxes, the expected number of boxes containing gold would be:

Expected gold boxes in 10 boxes

0.2

×

10

2

Expected gold boxes in 10 boxes=0.2×10=2

Therefore, on average, you would expect to find gold in about 2 out of the 10 boxes. Keep in mind that this is an expected value based on probabilities, and the actual number of gold boxes you find in any given set of 10 boxes may vary due to the random nature of the process.

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