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 [tex]\dfrac{14}{90}.[/tex] The theoretical probability of rolling 3 is [tex]\dfrac{1}{6}=\dfrac{15}{90}.[/tex] 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 [tex]\dfrac{16}{90}[/tex] and the theoretical probability of rolling 2 is [tex]\dfrac{1}{6}=\dfrac{15}{90}.[/tex] 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 [tex]\dfrac{12}{90}=\dfrac{2}{15}\neq \dfrac{2}{13}.[/tex] This option is false.

E. The experimental probability of rolling 1 is [tex]\dfrac{11}{90}[/tex] and the experimental probability of rolling 6 is [tex]\dfrac{17}{90}.[/tex] Since [tex]\dfrac{11}{90}<\dfrac{17}{90},[/tex] 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 · 2022-02-14T16:09:10+01:00

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:

[tex]P(4) = \frac{20}{90}[/tex]

Simplify

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

The experimental probability of rolling a 3 is:

[tex]P(3) = \frac{14}{90}[/tex]

Express as decimal

[tex]P(3) = 0.157[/tex]

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

The experimental probability of rolling a 2 is:

[tex]P(2) = \frac{16}{90}[/tex]

Express as decimal

[tex]P(2) = 0.178[/tex]

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

From the frequency table, we have:

[tex]P(5) = \frac{12}{90}[/tex]

Simplify

[tex]P(5) = \frac{4}{30}[/tex]-- 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