An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The problem asks for the empirical probability of rolling a 2 in the first 100 trials.
The table shows that a 2 was rolled 14 times in the first 100 trials.
Calculate the empirical probability: 100 14 = 0.14 .
The empirical probability of rolling a 2 is 0.14 .
Explanation
Understand the problem We are asked to find the empirical probability of rolling a 2 in the first 100 trials based on the provided table. The empirical probability is calculated by dividing the number of times the event occurred (rolling a 2) by the total number of trials.
Identify the number of successful trials From the table, we see that a 2 was rolled 14 times in the first 100 trials. Therefore, the empirical probability is the number of times a 2 was rolled divided by the total number of trials, which is 100.
Calculate the empirical probability To calculate the empirical probability, we divide the number of times a 2 was rolled (14) by the total number of trials (100): 100 14 = 0.14
State the final answer The empirical probability of rolling a 2 for the first 100 trials is 0.14.
Examples
In a real-world scenario, empirical probability can be used to estimate the likelihood of an event based on observed data. For example, if you wanted to know the probability of a specific product being defective, you could test a sample of products and calculate the empirical probability based on the number of defective items found in the sample. This probability can then be used to make predictions about the quality of future products. Suppose a quality control engineer tests 200 light bulbs and finds that 3 are defective. The empirical probability of a light bulb being defective is 200 3 = 0.015 , or 1.5%.
