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? 7/81 3/7 1/42 1/27

Explanation:

Step1: Identify probabilities

The probability of making a free - throw $P(F)=\frac{14}{18}=\frac{7}{9}$, and the probability of hitting the bullseye given a free - throw is made $P(B|F)=\frac{3}{9}=\frac{1}{3}$.

Step2: Use the multiplication rule for conditional probability

The multiplication rule for conditional probability is $P(F\cap B)=P(B|F)\times P(F)$.
Substitute the values: $P(F\cap B)=\frac{1}{3}\times\frac{7}{9}=\frac{7}{27}$.

Answer:

$\frac{7}{27}$