An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Probability of failing the driving test: 90 60 = 3 2 .
Probability of having under 20 driving lessons: 90 54 = 5 3 .
Probability of having under 20 driving lessons given passing the test: 30 9 = 10 3 .
Final Answers: 3 2 , 5 3 , 10 3 .
Explanation
Analyze the problem and data The problem provides a two-way table with data about 90 people who took a driving test. The table is categorized by whether they 'Passed' or 'Failed' and whether they had 'Under 20 driving lessons' or '20 or over driving lessons'. We need to find the probability of a randomly selected person failing, the probability of a randomly selected person having under 20 driving lessons, and the probability of a person who passed having under 20 driving lessons.
Calculate the probability of failing To find the probability that a randomly selected person failed their driving test, we divide the number of people who failed by the total number of people. From the table, 60 people failed out of a total of 90 people. So, the probability is: P ( Fail ) = Total number of people Number of people who failed = 90 60 Simplifying the fraction, we get: P ( Fail ) = 90 60 = 3 2
Calculate the probability of having under 20 driving lessons To find the probability that a randomly selected person had under 20 driving lessons, we divide the number of people with under 20 driving lessons by the total number of people. From the table, 54 people had under 20 driving lessons out of a total of 90 people. So, the probability is: P ( Under 20 ) = Total number of people Number of people with under 20 driving lessons = 90 54 Simplifying the fraction, we get: P ( Under 20 ) = 90 54 = 5 3
Calculate the conditional probability To find the probability that a person who passed had under 20 driving lessons, we divide the number of people who passed and had under 20 driving lessons by the total number of people who passed. From the table, 9 people passed and had under 20 driving lessons, and a total of 30 people passed. So, the probability is: P ( Under 20 ∣ Pass ) = Number of people who passed Number of people who passed and had under 20 driving lessons = 30 9 Simplifying the fraction, we get: P ( Under 20 ∣ Pass ) = 30 9 = 10 3
State the final answers (b) The probability that the person failed their driving test is 3 2 .
(c) The probability that the person had under 20 driving lessons is 5 3 .
(d) The probability that this person had under 20 driving lessons, given that they passed, is 10 3 .
Examples
Understanding probabilities from tables like this is useful in many real-world scenarios. For example, a driving school could use this data to understand the relationship between the number of lessons and the likelihood of passing the driving test. This information can help them tailor their teaching methods or advise students on the recommended number of lessons. Similarly, insurance companies might use such data to assess risk factors associated with different groups of drivers, potentially influencing insurance premiums.
The total charge delivered by the device is 450 coulombs, which corresponds to approximately 2.81 x 10^21 electrons flowing through it in 30 seconds.
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