The table shows the results of rolling a fair six-sided die. Complete parts (a) through (c) below.
| Outcome on Die | First 100 Trials | Second 100 Trials | 500 Trials |
|---|---|---|---|
| 1 | 18 | 15 | 84 |
| 2 | 14 | 19 | 88 |
| 3 | 19 | 14 | 86 |
| 4 | 21 | 16 | 79 |
| 5 | 14 | 12 | 89 |
| 6 | 14 | 24 | 74 |
(a) Using the table, find the empirical probability of rolling a 2 for the first 100 trials.
(b) Using the table, find the empirical probability of rolling a 2 for the second 100 trials.
(c) Using the table, find the empirical probability of rolling a 2 for 500 trials.
Answer (1)
Calculate the empirical probability: 500 88 = 0.176 .
Round the result to two decimal places.
The empirical probability of rolling a 2 for 500 trials is 0.18 .
Explanation
Analyze the problem and data Let's analyze the problem. We are given a table that shows the outcomes of rolling a fair six-sided die for different numbers of trials. We need to find the empirical probability of rolling a 2 for 500 trials. The table tells us that a 2 was rolled 88 times in 500 trials.
Calculate the empirical probability To find the empirical probability, we will divide the number of times a 2 was rolled by the total number of trials. In this case, the number of times a 2 was rolled is 88, and the total number of trials is 500. So, the empirical probability is: P ( 2 ) = Total number of trials Number of times 2 was rolled = 500 88
Calculate the fraction Now, let's calculate the value of the fraction: P ( 2 ) = 500 88 = 0.176
Round the result We need to round the result to two decimal places. Rounding 0.176 to two decimal places gives us 0.18.
State the final answer Therefore, the empirical probability of rolling a 2 for 500 trials is 0.18.
Examples
Imagine you are analyzing the performance of a baseball player. You want to know the probability that the player will hit a home run in their next at-bat. You can look at the player's past performance and calculate the empirical probability of hitting a home run based on the number of home runs they have hit in the past divided by the total number of at-bats. This gives you an estimate of the player's likelihood of hitting a home run in the future.
