Question

rochelle conducts an experiment by rolling a fair number cube 120 times to explore probabilities of each outcome. the results of rochelles rolls are summarized in the frequency table: outcome 1 2 3 4 5 6 frequency 16 23 15 15 20 15 which statement is correct? outcome 1 has the same experimental probability and theoretical probability. outcome 2 has the same experimental probability and theoretical probability. outcome 3, 4, and 6 have the same experimental probability which matches the theoretical probability. outcome 5 has the same experimental probability and theoretical probability.

Explanation:

Step1: Calculate theoretical probability

For a fair number - cube, the theoretical probability of each outcome is $\frac{1}{6}$ since there are 6 possible outcomes.

Step2: Calculate experimental probabilities

The experimental probability of an outcome is calculated as $P=\frac{\text{Frequency}}{\text{Total number of trials}}$. The total number of trials is $16 + 23+15 + 15+20 + 15=104$ (there is a mistake above, it should be 120).

• For outcome 1: $P_1=\frac{16}{120}=\frac{2}{15}

eq\frac{1}{6}$

• For outcome 2: $P_2=\frac{23}{120}

eq\frac{1}{6}$

• For outcome 3: $P_3=\frac{15}{120}=\frac{1}{8}

eq\frac{1}{6}$

• For outcome 4: $P_4=\frac{15}{120}=\frac{1}{8}

eq\frac{1}{6}$

• For outcome 5: $P_5=\frac{20}{120}=\frac{1}{6}$
• For outcome 6: $P_6=\frac{15}{120}=\frac{1}{8}

eq\frac{1}{6}$

Answer:

Outcome 5 has the same experimental probability and theoretical probability.