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If you roll a $6$ -sided die $6$ times, what is the best prediction possible for the number of times you will roll an even number? $\newline$ $\_\_\_\_$ times

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Full solution

Q. If you roll a

6

-sided die

6

times, what is the best prediction possible for the number of times you will roll an even number?

\newline

\_\_\_\_

times

Calculate probability: Calculate the probability of rolling an even number on a $6$ -sided die. $\newline$ There are $3$ even numbers ( $2$ , $4$ , $6$ ) on a $6$ -sided die. $\newline$ Probability $(P)$ of rolling an even number $= \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}.$
Predict even rolls: Use the probability to predict the number of even rolls in $6$ trials. $\newline$ Expected number of even rolls = Probability of even number $\times$ Number of rolls = $\frac{1}{2} \times 6 = 3$ .

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