An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The problem provides a conditional relative frequency table.
We identify the required probability: P(Purchased at Box Office | More than $30). - From the table, P(Purchased at Box Office | More than 30 ) = 0.14 . - The probability that Lorenzo purchased the ticket at the box office, given that he paid more than 30 , i s \boxed{0.14}$.
Explanation
Understand the problem We are given a conditional relative frequency table that compares the cost of a ticket and the method of purchase. We want to find the probability that a ticket was purchased at the box office, given that the ticket cost more than $30.
Identify the relevant probability The table provides the conditional relative frequencies directly. We are looking for the probability P(Purchased at Box Office | More than $30). From the table, we can see that this value is 0.14.
State the final answer Therefore, the probability that Lorenzo purchased the ticket at the box office, given that he paid more than $30 for the ticket, is 0.14.
Examples
Conditional probability is used in many real-life scenarios, such as in medical diagnosis. For example, given that a patient tests positive for a disease, what is the probability that they actually have the disease? This requires understanding the sensitivity and specificity of the test, as well as the prevalence of the disease in the population. Similarly, in marketing, conditional probability can be used to determine the probability that a customer will purchase a product, given that they have viewed an advertisement.
In 30 seconds, an electric device delivering 15.0 A of current transfers roughly 2.81 × 1 0 21 electrons. This is calculated by determining the total charge and then converting that charge into the number of electrons based on the charge of a single electron. Understanding the relationship between current, charge, and time is crucial in this calculation.
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