Question

question 5
2 pts
a die was rolled 96 times and the results are shown below

outcome	1	2	3	4	5	6
frequency	14	22	6	26	12	16

which of the 6 outcomes has the same experimental probability as its theoretical probability?

Explanation:

Step1: Calculate theoretical probability

For a fair - die, the theoretical probability of each outcome is $\frac{1}{6}$.

Step2: Calculate experimental probabilities for each outcome

The experimental probability $P(X)$ of an outcome $X$ is given by $P(X)=\frac{\text{Frequency of }X}{\text{Total number of trials}}$. The total number of trials is $n = 96$.
For outcome 1: $P(1)=\frac{14}{96}=\frac{7}{48}$
For outcome 2: $P(2)=\frac{22}{96}=\frac{11}{48}$
For outcome 3: $P(3)=\frac{6}{96}=\frac{1}{16}$
For outcome 4: $P(4)=\frac{26}{96}=\frac{13}{48}$
For outcome 5: $P(5)=\frac{12}{96}=\frac{1}{8}$
For outcome 6: $P(6)=\frac{16}{96}=\frac{1}{6}$

Answer:

6