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

Mathematics

2 answers:

Sergeeva-Olga [200]2 years ago

8 0

Answer:

True statements:

A. The relative frequency of rolling 4 is $\dfrac{2}{9}.$

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

Step-by-step explanation:

Nathan made 11 + 16 + 14 + 20 + 12 + 17 = 90 rolls altogether. Consider all options:

A. The relative frequency of rolling 4 is

$\dfrac{20}{90}=\dfrac{2}{9}.$

This option is true.

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 $\dfrac{12}{90}=\dfrac{2}{15}\neq \dfrac{2}{13}.$ 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 $\dfrac{11}{90}$ then the experimental probability of rolling 1 is less than the experimental probability of rolling 6. This option is true.