Question

An urn has m blue balls and n red balls. You randomly pick the balls one by one and lay them in a line. What is the probability that the last ball is red?

Answer 1

To find the probability that the last ball selected is red, we need to consider two cases: when the first ball selected is red and when the first ball selected is blue. By calculating the probabilities in each case and adding them together, we can determine the overall probability.

Step-by-step explanation:

To find the probability that the last ball selected is red, we need to consider two cases:

Case 1: The first ball selected is red.

In this case, there are a total of (m+n) balls in the urn, with (n-1) red balls and m blue balls. The probability of selecting a red ball next is (n-1)/(m+n-1).

Case 2: The first ball selected is blue.

In this case, there are still (m+n) balls in the urn, but now there are n red balls and (m-1) blue balls. The probability of selecting a red ball next is n/(m+n-1).

Since these two cases are mutually exclusive, we can add their probabilities to find the overall probability:

P(last ball is red) = P(first ball is red) * P(second ball is red | first ball is red) + P(first ball is blue) * P(second ball is red | first ball is blue)