An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The total charge delivered by the electric device is 450 C , which corresponds to approximately 2.81 × 1 0 21 electrons flowing through it in 30 seconds.
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Define events: A = individual is 35-44, B = less likely to buy.
Use conditional probability formula: P ( B ∣ A ) = P ( A ) P ( A and B ) .
Extract values from the table: 6 individuals are 35-44 and less likely to buy, 531 total individuals are 35-44.
Calculate: P ( B ∣ A ) = 531 6 ≈ 0.011 .
Explanation
Understand the problem We are asked to find the probability that a randomly selected individual is less likely to buy a product emphasized as 'Made in America,' given the individual is 35 to 44 years of age. This is a conditional probability problem.
Define events and conditional probability Let A be the event that a randomly selected individual is in the 35-44 age group. Let B be the event that a randomly selected individual is less likely to buy a product emphasized as 'Made in America'. We want to find P(B|A), which is the probability that an individual is less likely to buy the product given that they are in the 35-44 age group. P(B|A) = P(A and B) / P(A)
Identify values from the table From the table, the number of individuals who are 35-44 and less likely to buy the product is 6. The total number of individuals who are 35-44 is 531.
Apply the conditional probability formula P(B|A) = (Number of individuals who are 35-44 and less likely to buy) / (Total number of individuals who are 35-44) P(B|A) = 6 / 531
Calculate the probability Calculating the probability: P ( B ∣ A ) = 531 6 ≈ 0.011299
Round the result Rounding to three decimal places, the probability is approximately 0.011.
Examples
Conditional probability is used in marketing to determine the likelihood of a customer taking a specific action (e.g., making a purchase) given that they have already taken another action (e.g., clicking on an ad). For example, a company might want to know the probability that a customer will buy a product given that they have visited the company's website. This information can be used to target marketing efforts more effectively.
