Question

a survey of the 12th - grade students at gulfport 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% 20%

Explanation:

Step1: Recall 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. We are given $P(B) = 84\%=0.84$, $P(A\cap B)=14\% = 0.14$.

Step2: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.14}{0.84}=\frac{1}{6}\approx0.1667$.

Step3: Convert to percentage

Multiply the result by 100 to get the percentage: $0.1667\times100 = 16.67\%$. Rounding to the nearest whole - percent, we get $17\%$.

Answer:

17%