Desmond is rolling a standard six-sided number cube. He plans to roll it $72$ times.

1. About how many times would you expect Desmond to roll a $4$? Why?

   Hint (a):

   On a six sided dice, if six possible outcomes are equally likely, what is the probability that you will roll a $4$?

   More Help (a):

   If you multiplied this probability by the total number of rolls, $72$, how many rolls would you expect Desmond to roll a $4$?

   Answer (a):

   About $12$ times.
   Be sure to know why this is the answer.

2. About how many times would you expect him to roll an even number? Why?

   Hint (b):

   On a six sided dice, half of the numbers:
   $2, 4,$ and $6$ are even.

   More Help (b):

   If three numbers out of six are even, what would the probability of rolling an even number be? Multiply this number by the $72$ rolls to find the expected number of rolls that would be even.

3. Desmond kept track of his results for all $72$ rolls. The chart below shows some of his results.
   

   Result	Number of outcomes
   $1$	$9$
   $2$	$14$
   $3$	$11$
   $4$	$8$

   
   Based on his partial results, how many times did he roll a $5$ or a $6$?

   Hint (c):

   If the total number of rolls is $72$, and $42$ of the rolls resulted in the numbers $1-4$, how many times must Desmond have rolled $5$ or $6$?

   Answer (c):

   $30$ times