GATE-2024-CS1(Forenoon)

Given:
Total number of red balls: 10
Total number of blue balls: 15
Total balls: 25
Two balls are drawn randomly without replacement.
The first ball drawn is red.
Let’s denote:
A = Event that the first ball drawn is red.
B = Event that both balls drawn are red.
We need to find P(B|A), the probability that both balls are red given that the first ball is red.

Total number of ways to draw two balls:
Since the first ball is known to be red, we need to find the probability of drawing another red ball from the remaining balls.

Remaining Balls After First Draw:

After drawing the first red ball, there are 9 red balls and 15 blue balls left.
Total remaining balls = 24
Probability of Drawing a Second Red Ball:
The number of favorable outcomes for drawing another red ball is 9 (since there are 9 red balls left).
The total number of outcomes is 24 (total remaining balls).
So, the probability of drawing a second red ball given that the first one was red is:
P(Second ball is red |First ball is red)= Number of remaining red balls
​/ Total remaining balls = 9/24=0.375