Nathan rolls a number cube and records the result of each roll in the table.

Which statements below represent the situation? Choose all that apply.

The relative frequency of rolling a 4 is 2/9.

The experimental probability of rolling a 3 is greater than the theoretical probability of rolling a 3.

The experimental probability of rolling a 2 is greater than the theoretical probability of rolling a 2.

The relative frequency of rolling a 5 is 2/13.

The experimental probability of rolling a 1 is less than the experimental probability of rolling a 6.

The theoretical probability of rolling a 1 is less than the theoretical probability of rolling a 6.

B. The experimental probability of rolling 3 is \(\dfrac{14}{90}.\) The theoretical probability of rolling 3 is \(\dfrac{1}{6}=\dfrac{15}{90}.\) therefore, the experimental probability of rolling 3 is less than the theoretical probability. This option is false.

C. The experimental probability of rolling 2 is \(\dfrac{16}{90}\) and the theoretical probability of rolling 2 is \(\dfrac{1}{6}=\dfrac{15}{90}.\) The experimental probability of rolling 2 is smaller than the theoretical probability of rolling 2. Option C is false.

D. The relative frequency of rolling 5 is \(\dfrac{12}{90}=\dfrac{2}{15} eq \dfrac{2}{13}.\) This option is false.

E. The experimental probability of rolling 1 is \(\dfrac{11}{90}\) and the experimental probability of rolling 6 is \(\dfrac{17}{90}.\) Since \(\dfrac{11}{90}<\dfrac{17}{90},\) then the experimental probability of rolling 1 is less than the experimental probability of rolling 6. This option is true.

F. The theoretical probability of rolling 1 is the same as the theoretical probability of rolling 6. This option is false.

MrRoyal MrRoyal · Answer 2 · 2022-02-14T10:09:10-05:00

The true statements are:

(a) The relative frequency of rolling a 4 is 2/9.
(c) The experimental probability of rolling a 2 is greater than the theoretical probability of rolling a 2.
(d) The experimental probability of rolling a 1 is less than the experimental probability of rolling a 6.

From the frequency table, we have:

\(P(4) = \frac{20}{90}\)

Simplify

\(P(4) = \frac{2}{9}\) -- this represents the relative frequency of rolling a 4

The experimental probability of rolling a 3 is:

\(P(3) = \frac{14}{90}\)

Express as decimal

\(P(3) = 0.157\)

The above is less than the theoretical probability of rolling a 3 (i.e. 0.167)

The experimental probability of rolling a 2 is:

\(P(2) = \frac{16}{90}\)

Express as decimal

\(P(2) = 0.178\)

The above is greater than the theoretical probability of rolling a 2 (i.e. 0.167)

From the frequency table, we have:

\(P(5) = \frac{12}{90}\)

Simplify

\(P(5) = \frac{4}{30}\)-- this represents the relative frequency of rolling a 5

Also, from the table:

The experimental probability of rolling a 1 is less than the experimental probability of rolling a 6.

This is so, because the frequency of 1 is less than the frequency of 6

Also,

The theoretical probability of rolling a 1 is the same as the theoretical probability of rolling a 6