Question

You rolled a six-sided dice 6 times and you rolled two 5's in your 6 rolls. Does the experimental probability match the theoretical probability of rolling a 5?
Group of answer choices

No

Yes

You would need more rolls to find out

Not enough info

Answer 1

To determine if the experimental probability matches the theoretical probability of rolling a 5 on a six-sided die, we need to first look at the theoretical probability.

The theoretical probability of rolling a 5 on a six-sided die is given by:

\[
P(rolling\ a\ 5) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6}
\]

In your experiment, you rolled the die 6 times and rolled two 5's. Hence, the experimental probability of rolling a 5 is:

\[
P_{experimental} = \frac{\text{Number of times 5 was rolled}}{\text{Total rolls}} = \frac{2}{6} = \frac{1}{3}
\]

Now, we compare the experimental probability \(\frac{1}{3}\) with the theoretical probability \(\frac{1}{6}\).

Since \(\frac{1}{3} \neq \frac{1}{6}\), the experimental probability does not match the theoretical probability.

Therefore, the correct answer is:

**No**