Question

question 7 of 8 select the correct answer. samantha is conducting an experiment and has to make a free throw and throw a dart for a bullseye. the probability of accomplishing both is 3 out of 9. the probability of making the free - throw is 14 out of 18. given the free - throw is made, what is the probability of hitting the bullseye?

Explanation:

Step1: Identify probabilities of individual events

The probability of making a free - throw, $P(F)=\frac{14}{18}=\frac{7}{9}$. The probability of hitting the bullseye given a free - throw is made, $P(B|F)=\frac{3}{9}$.

Step2: Use the formula for conditional probability

The probability of both events occurring (making a free - throw and hitting the bullseye) is given by the formula $P(F\cap B)=P(F)\times P(B|F)$. Substitute the values: $P(F\cap B)=\frac{7}{9}\times\frac{3}{9}=\frac{7\times3}{9\times9}=\frac{21}{81}=\frac{7}{27}$.

Answer:

$\frac{7}{27}$