Question

There are two identical boxes. Box I contains 5 red and 4 black balls, while Box II contains 3 red and 3 black balls. A person choose a box at random and takes out a ball. 

(a) Find the probability that the ball drawn is red. 

(b) If the ball drawn is black, what is the probability that it is drawn from Box II.

Answer 1

(a) Let E₁ be the event selecting box I and E₂ be the event selecting box II.

\(P\left(A / E_{1}\right)=\frac{1}{2} \times \frac{5}{9}=\frac{5}{18}\)

\(P\left(A / E_{2}\right)=\frac{1}{2} \times \frac{3}{6}=\frac{3}{12}\)

P (taking a red ball) 

\(\frac{5}{18}+\frac{3}{12}=\frac{19}{36}\)

b) Let B be the event selecting a black ball