Question

Empirical Method: A die is rolled 850 times. On 85 of those rolls, the die comes up 1 . Use the Empirical method to approximate the probability that the die comes up . Round your answer to four decimal places as necessary.

Answer 1

To approximate the probability of the die coming up with a specific outcome (in this case, a 1) using the empirical method, we can use the following formula:

\[
P(\text{outcome}) \approx \frac{\text{Number of times outcome occurs}}{\text{Total number of trials}}
\]

Given that the die was rolled 850 times and it came up with a 1 a total of 85 times, we can plug these numbers into the formula:

\[
P(1) \approx \frac{85}{850}
\]

Now we calculate the fraction:

\[
P(1) \approx \frac{85}{850} = 0.1
\]

To round this to four decimal places, we keep it as:

\[
P(1) \approx 0.1000
\]

Thus, the approximate probability that the die comes up 1 is:

\[
\boxed{0.1000}
\]