Number cube

Question

Eliot has a number cube that is numbered from 1 to 6. There is a different number on each side of the cube. If Elliot rolls the cube 50 times, predict how many times you would expect the side with the number 2 to land face up.

Answer 1

A number cube, eh? Are they trying to confuse us by not calling it a die? :)

 

Let's assume this is a fair number cube. By fair, I mean each side is equally likely to land face up. That means each side has a one in six chance of landing face up for any roll.

 

For this problem, the number 2 will have a 1/6 chance of landing face up for each and every roll. After six rolls, we will probably have rolled the number 2 once, since 1/6+1/6+1/6+1/6+1/6+1/6=1. For this problem, we can add up 1/6 for any number of rolls and find out how many we will probably roll, but I don't want to repeat addition 50 times. Thankfully multiplication is the same as repeated addition, so by the end of the 50th roll, we find with multiplication:

(1/6)(50)=50/6=8.333

 

It couldn't have rolled face up 8.333 times, so I would probably answer 8 times, since 8.333 is closer to 8 than to 9.