Cam is going to roll a fair $6$ -sided die $2400$ times. $\newline$ What is the best prediction for the number of times that Cam will roll the number $4$ ? $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $400$ times $\newline$ (B) Close to $400$ times but probably not exactly $400$ times $\newline$ (C) Exactly $600$ times $\newline$ (D) Close to $600$ times but probably not exactly $600$ times

Full solution

Q. Cam is going to roll a fair

6

-sided die

2400

times.

\newline

What is the best prediction for the number of times that Cam will roll the number

4

\newline

Choose

1

answer:

\newline

(A) Exactly

400

times

\newline

(B) Close to

400

times but probably not exactly

400

times

\newline

600

times

\newline

(D) Close to

600

times but probably not exactly

600

times

Understand the problem: Understand the problem. $\newline$ We need to predict how many times the number $4$ will appear when a fair $6$ -sided die is rolled $2400$ times.
Calculate expected frequency: Calculate the expected frequency for the number $4$ . Since the die is fair, each of the six faces has an equal chance of landing face up. Therefore, the probability of rolling a $4$ on any given roll is $\frac{1}{6}$ .
Use probability to predict: Use the probability to predict the number of times $4$ will be rolled. $\newline$ To find the expected number of times $4$ will be rolled, multiply the total number of rolls by the probability of rolling a $4$ . $\newline$ Expected number of times rolling a $4$ $=$ Total number of rolls $*$ Probability of rolling a $4$ $\newline$ Expected number of times rolling a $4$ $= 2400 \times \left(\frac{1}{6}\right)$
Perform the calculation: Perform the calculation. $\newline$ Expected number of times rolling a $4 = 2400 \times \left(\frac{1}{6}\right) = 400$
Interpret the result: Interpret the result. $\newline$ The calculation shows that the expected number of times rolling a $4$ is $400$ . However, due to the nature of probability and randomness, it is unlikely to be exactly $400$ . It will be close to $400$ , but the actual number will probably vary due to chance.