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

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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Find probabilities using combinations and permutations

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: Understand the probability of rolling a number greater than $4$ on a $6$ -sided die. There are two numbers greater than $4$ on a $6$ -sided die: $5$ and $6$ . Therefore, the probability of rolling a number greater than $4$ is the number of favorable outcomes (rolling a $5$ or $6$ ) divided by the total number of possible outcomes ( $1$ through $6$ ). Probability = Number of favorable outcomes / Total number of possible outcomes Probability = $\frac{2}{6}$ Probability = $\frac{1}{3}$
Predict Rolls Based on Probability: Use the probability to predict the number of times a number greater than $4$ will be rolled in $180$ rolls. $\newline$ To find the expected number of times a number greater than $4$ will be rolled, multiply the total number of rolls by the probability of rolling a number greater than $4$ . $\newline$ Expected number of times $=$ Total rolls $\times$ Probability $\newline$ Expected number of times $= 180 \times (1 / 3)$
Calculate Expected Number: Calculate the expected number of times a number greater than $4$ will be rolled. $\newline$ Expected number of times = $180 \times (1 / 3)$ $\newline$ Expected number of times = $180 / 3$ $\newline$ Expected number of times = $60$
Determine Best Prediction: Determine the best prediction based on the expected value. $\newline$ The best prediction for the number of times Jeremy will roll a number greater than $4$ is close to the expected value, which is $60$ times. However, due to the nature of probability and randomness, it is unlikely to be exactly $60$ times. Therefore, the best prediction is that Jeremy will roll a number greater than $4$ close to $60$ times but probably not exactly $60$ times.

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