A bag contains $5$ red and $4$ blue balls. Two balls are drawn at random one by one without replacement. What is the probability that the second ball is blue given that the first ball was red?

Solution

1. Initially, the bag contains $5$ red and $4$ blue balls, totaling $9$ balls.
2. After drawing one red ball, the bag contains $4$ red and $4$ blue balls, totaling $8$ balls.
3. The probability of drawing a blue ball from the remaining $8$ balls is $4/8 = 1/2$.
4. Hence the answer is (B).