An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the total number of students given four quarters: 32 + 19 = 51 .
Calculate the probability of a student spending the money, given four quarters: 51 32 ≈ 0.627 .
Calculate the probability of a student keeping the money, given four quarters: 51 19 ≈ 0.373 .
The probabilities are approximately 0.627 and 0.373 , respectively.
Explanation
Understanding the Problem Let's break down this probability problem step by step! We're given a table that summarizes an experiment where college students were given either four quarters or a $$1 bill and could choose to either keep the money or spend it on gum. We need to find two probabilities related to this experiment.
Calculating the Probability (Part a) Part a asks for the probability of randomly selecting a student who spent the money, given that the student was given four quarters. To solve this, we need to look at the row in the table corresponding to students given four quarters. We see that 32 of these students purchased gum. The total number of students given four quarters is the sum of those who purchased gum and those who kept the money, which is 32 + 19 = 51 . Therefore, the probability is the number of students who purchased gum divided by the total number of students given four quarters.
Finding the Probability (Part a) So, the probability of a student spending the money (purchasing gum), given that they received four quarters, is: 51 32 ≈ 0.627
Calculating the Probability (Part b) Part b asks for the probability of randomly selecting a student who kept the money, given that the student was given four quarters. Again, we focus on the row in the table for students given four quarters. We see that 19 of these students kept the money. As we calculated before, the total number of students given four quarters is 32 + 19 = 51 . Therefore, the probability is the number of students who kept the money divided by the total number of students given four quarters.
Finding the Probability (Part b) So, the probability of a student keeping the money, given that they received four quarters, is: 51 19 ≈ 0.373
Final Answer Therefore, the probability of randomly selecting a student who spent the money, given that the student was given four quarters, is approximately 0.627, and the probability of randomly selecting a student who kept the money, given that the student was given four quarters, is approximately 0.373.
Examples
This type of probability calculation is useful in market research. For example, a company might want to know the probability that a customer will purchase a product given that they received a coupon. The company can use this information to decide whether or not to send out coupons in the future. Let's say a store gives out coupons for a new brand of coffee. They track whether people who received coupons actually bought the coffee. By calculating conditional probabilities, they can see if the coupon made a difference in purchasing behavior.
