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Jeremy is going to roll a fair $6$ -sided die $180$ times. $\newline$ What is the best prediction for the number of times that Jeremy will roll a number greater than $4$ ? $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $30$ times $\newline$ (B) Close to $30$ times but probably not exactly $30$ times $\newline$ (C) Exactly $60$ times $\newline$ (D) Close to $60$ times but probably not exactly $60$ times

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Make predictions

Full solution

Q. Jeremy is going to roll a fair

6

-sided die

180

times.

\newline

What is the best prediction for the number of times that Jeremy will roll a number greater than

4

?

\newline

Choose

1

answer:

\newline

(A) Exactly

30

times

\newline

(B) Close to

30

times but probably not exactly

30

times

\newline

(C) Exactly

60

times

\newline

(D) Close to

60

times but probably not exactly

60

times

Understand Probability: To solve this problem, we need to understand the probability of rolling a number greater than $4$ on a $6$ -sided die. The numbers greater than $4$ on a $6$ -sided die are $5$ and $6$ . There are $2$ favorable outcomes out of $6$ possible outcomes. $\newline$ Probability of rolling a number greater than $4$ $= \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} = \frac{1}{3}.$
Predict Number of Rolls: Next, we use the probability to predict the number of times Jeremy will roll a number greater than $4$ in $180$ rolls. We multiply the total number of rolls by the probability of rolling a number greater than $4$ . $\newline$ Predicted number of times = Total rolls $\times$ Probability = $180 \times (1 / 3)$ .
Calculate Predicted Times: Now, we calculate the predicted number of times. $\newline$ Predicted number of times = $180 \times (1 / 3) = 180 / 3 = 60$ .
Consider Fairness and Independence: Since the die is fair and the rolls are independent, the actual number of times Jeremy rolls a number greater than $4$ can vary. However, the best prediction based on probability is $60$ times. This means that while Jeremy might not roll a number greater than $4$ exactly $60$ times, it is the most likely outcome over a large number of trials.

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