What is the probability of rolling a 4 three times in a roll on a fair sided die if you roll it ten times

Question

It is a question that I need help with in math

Answer 1

Hi Jason,

 

To calculate this type of probability, you first consider the probability of having exactly what you are looking for; in this situation, that would be rolling a 4 three times, then not rolling a 4 the remaining seven times.

 

Once you have that probability, you need to correct for the fact that the order doesn't matter. That last phrase sounds a lot like combinations, and it is! You take the probability from the first part and multiply it by the number of ways you can roll those ten tries, getting a 4 three times. You don't have to account for the other rolls that don't give a 4 because they are just everything that isn't a 4.

 

This should lead you to the correct calculation,

 

Jim S.