Question

A jar containing 8 marbles of which 4 red and 4 blue marbles are there. Find the probability of getting a red given the first one was red too.

(a) \(\frac{4}{13}\)

(b) \(\frac{2}{11}\)

(c) \(\frac{3}{7}\)

(d) \(\frac{8}{15}\)

I have been asked this question in unit test.

My doubt is from Discrete Probability in chapter Discrete Probability of Discrete Mathematics

Answer 1

Correct choice is (c) \(\frac{3}{7}\)

To explain: Suppose, P (A) = getting a red marble in the first turn, P (B) = getting a black marble in the second turn. P (A) = \(\frac{4}{8}\) and P (B) = \(\frac{3}{7}\) and P (A and B) = \(\frac{4}{8}*\frac{3}{7} = \frac{3}{14}\) P(B/A) = \(\frac{P(A \,and \,B)}{P(A)} = \frac{\frac{3}{14}}{\frac{1}{2}} = \frac{3}{7}\).