question 5\n2 pts\na die was rolled 96 times and the results are shown below\n| outcome | 1 | 2 | 3 | 4 | 5…
question 5\n2 pts\na die was rolled 96 times and the results are shown below\n| outcome | 1 | 2 | 3 | 4 | 5 | 6 |\n| frequency | 14 | 22 | 6 | 26 | 12 | 16 |\nwhich of the 6 outcomes has the same experimental probability as its theoretical probability?
Answer
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