Conditional probability problem for 5 red balls and 5 blue balls in a bag

Question

A bag contains 5 red balls and 5 blue balls. Three balls are drawn randomly without replacement.
Find: the conditional probability of drawing at least 1 blue ball if we had already drew at least one red ball.

Answer 1

⚠️ I wrote this assuming that you are not satisfied with this answer and want a different answer
️ This answer is with a different approach and may be wrong.

Probability = 2/3

According to the condition,
it is fixed that we had already drawn a red ball.
So we can say that - now we are left only with the possible combination from 2 balls.
These 2 balls can be in combination of

• red-blue (or blue-red both are same)
• red-red
• blue-blue
  
  Only in 2 out of 3 combinations, we get at least 1 blue ball.
  
  (Just don't forget that we are ignoring the 3rd ball as it is already been told that it is red.)