Question

Paige rolls a number cube sixty-four times. The number 4 comes up fourteen times. The number 3 comes up six times. Rounded to the nearest whole percent, what is the experimental probability of rolling a 3 or 4?

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Answer 1

To find the experimental probability of rolling a 3 or a 4, we first need to determine the total number of times either number was rolled.

Paige rolled a:
- Number 4: 14 times
- Number 3: 6 times

The total occurrences of rolling a 3 or a 4 is:

\[
14 (for\ 4) + 6 (for\ 3) = 20
\]

Next, we know that she rolled the number cube a total of 64 times. The experimental probability \( P \) of rolling a 3 or a 4 is given by the formula:

\[
P(3\ or\ 4) = \frac{\text{Number of times 3 or 4 was rolled}}{\text{Total rolls}} = \frac{20}{64}
\]

To simplify \( \frac{20}{64} \):

\[
\frac{20}{64} = \frac{5}{16}
\]

Next, we calculate the decimal value of \( \frac{5}{16} \):

\[
\frac{5}{16} = 0.3125
\]

Now, we convert this decimal to a percentage by multiplying by 100:

\[
0.3125 \times 100 = 31.25\%
\]

Finally, rounding to the nearest whole percent:

\[
31.25\% \approx 31\%
\]

Thus, the experimental probability of rolling a 3 or a 4, rounded to the nearest whole percent, is:

\[
\boxed{31\%}
\]