A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is ________

Let $R_1$ be the event that the first ball drawn is red, and $R_2$ be the event that the second ball drawn is red.

We need to find the conditional probability $P(R_1 \cap R_2 \mid R_1)$:

Initially, the bag has $10$ red balls and $15$ blue balls (total $25$ balls).

Given that the first ball drawn is red, there are now:

• $9$ red balls remaining

• $15$ blue balls remaining

• Total $24$ balls remaining

The probability that the second ball is also red given the first is red is:

Rounded to 3 decimal places, the probability is 0.375.