Question

a survey of the 12th grade students at gaffigan high school found that 84% of the seniors have their drivers licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have drivers licenses and take the bus to school every day. to the nearest whole percent, what is the probability that a senior takes the bus to school every day, given that he or she has a drivers license? 17% 19% 36% 70%

Explanation:

Step1: Recall the conditional probability formula

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that a senior takes the bus to school every day and \(B\) be the event that a senior has a driver's license.

Step2: Substitute the given values into the formula

We are given that \(P(B) = 0.84\) (probability of having a driver's license) and \(P(A\cap B)=0.14\) (probability of having a driver's license and taking the bus). Then \(P(A|B)=\frac{0.14}{0.84}\).

Step3: Calculate the value

\(\frac{0.14}{0.84}=\frac{14}{84}=\frac{1}{6}\approx0.1667\).

Step4: Convert to percentage

Multiply by \(100\) to get the percentage: \(0.1667\times100 = 16.67\%\approx17\%\).

Answer:

17%