An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the conditional probability P ( 45 − 54 years old ∣ more likely ) using the formula P ( A ∣ B ) = P ( B ) P ( A ∩ B ) .
Find P ( 45 − 54 years old ∩ more likely ) = 2143 359 .
Find P ( more likely ) = 2143 1322 .
Calculate P ( 45 − 54 years old ∣ more likely ) = 1322 359 ≈ 0.272 . The final answer is 0.272 .
Explanation
Understand the problem and provided data We are given a contingency table showing the results of a survey about whether people are more or less likely to buy products 'Made in America', broken down by age group. We are asked to find P ( 45 − 54 years old ∣ more likely ) and determine if the events '45-54 years old' and 'more likely' are independent.
Conditional Probability Formula To find P ( 45 − 54 years old ∣ more likely ) , we use the conditional probability formula: P ( A ∣ B ) = P ( B ) P ( A ∩ B ) In this case, A is the event '45-54 years old' and B is the event 'more likely'.
Find the joint probability First, we need to find P ( 45 − 54 years old ∩ more likely ) . This is the probability that a person is both 45-54 years old and more likely to buy products 'Made in America'. From the table, we see that there are 359 people who fit this description. The total number of respondents is 2143. Therefore, P ( 45 − 54 years old ∩ more likely ) = 2143 359
Find the probability of 'more likely' Next, we need to find P ( more likely ) . This is the probability that a person is more likely to buy products 'Made in America'. From the table, we see that there are 1322 people who are more likely to buy. The total number of respondents is 2143. Therefore, P ( more likely ) = 2143 1322
Calculate the conditional probability Now we can calculate the conditional probability: P ( 45 − 54 years old ∣ more likely ) = P ( more likely ) P ( 45 − 54 years old ∩ more likely ) = 2143 1322 2143 359 = 1322 359 ≈ 0.272
Check for independence To determine if the events '45-54 years old' and 'more likely' are independent, we need to check if: P ( 45 − 54 years old ∣ more likely ) = P ( 45 − 54 years old ) We are given that P ( 45 − 54 years old ) = 0.252 . We calculated that P ( 45 − 54 years old ∣ more likely ) ≈ 0.272 . Since these probabilities are not equal, the events are not independent.
Final Answer Therefore, P ( 45 − 54 years old ∣ more likely ) = 1322 359 ≈ 0.272 . The events '45-54 years old' and 'more likely' are not independent.
Examples
Understanding conditional probabilities is very useful in marketing. For example, a company might want to know the probability that a customer will buy a product given that they have seen an advertisement. This can help the company to target its advertising more effectively. In this case, knowing P ( 45 − 54 years old ∣ more likely ) helps understand the buying behavior of a specific age group, given they are already inclined to buy 'Made in America' products. This information can be used to tailor marketing campaigns specifically to this demographic.
In 30 seconds, a current of 15.0 A delivers approximately 2.81 x 10^{21} electrons. This is calculated using the relationship between current, charge, and the charge of a single electron. The total charge of 450 Coulombs is divided by the electron charge to find the number of electrons.
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