Answer :
Final answer:
The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.
Explanation:
To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.
We can use the formula:
P(A|B) = P(A and B) / P(B)
where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.
In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.
Plugging in the values into the formula:
P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)
P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667
To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.
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To the nearest whole percent, the probability that a senior takes the bus to school every day, given that they have a driver's license, is approximately 17%.
To find the probability that a senior takes the bus to school every day, given that they have a driver's license, you can use the concept of conditional probability. The probability of A given B is denoted as P(A | B) and is calculated as:
P(A | B) = P(A and B) / P(B)
In this case, A represents "takes the bus to school every day" and B represents "has a driver's license."
Given the information from the survey:
- P(A) = 16% (probability of taking the bus to school every day)
- P(B) = 84% (probability of having a driver's license)
- P(A and B) = 14% (probability of both having a driver's license and taking the bus to school every day)
Now, you can calculate the conditional probability:
P(A | B) = P(A and B) / P(B)
P(A | B) = 14% / 84% ≈ 0.1667 (rounded to four decimal places)
To express this probability as a percentage, multiply by 100:
P(A | B) ≈ 16.67%
So, to the nearest whole percent, the probability that a senior takes the bus to school every day, given that they have a driver's license, is approximately 17%.
To know more about probability, refer here:
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