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5-49.

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?

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

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

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?

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

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 $6$?

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 $6$?

$30$ times Explore the problem with the eTool below.
Click the link at right for the full version of the eTool: MC2 5-49 HW eTool