A bag contains an unknown number of red balls and yellow balls. When N balls are drawn at random (without replacement) the probability that they are all yellow is 1/2. The number of balls in the bag is the minimum for this to happen.

If the first N balls were all yellow, what is the probability that the next ball drawn is red?

Express the probability as a function of N.

(In reply to re: some exceptions by Steve Herman)

With the notation that this is the minimum that this could happen, the answer is 1/2, as N would need to be 2 in order to refer to "all yellow", not referring to 1 as "all". On the other hand if "all" is allowed to refer to a single yellow ball, then the probability the next one is red is 1.

Posted by Charlie on 2024-04-17 07:48:18