Question

A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second.

What are the following probabilities?

P(B) =

P(R | B) =

P(B ∩ R) =

The probability that the first ball chosen is black and the second ball chosen is red is about
percent.

Answer 1

P(B) = 8/12 = 2/3 ≈ 66.67%

P(R | B) = 4/11 ≈ 36.36%

P(B ∩ R) = P(B)·P(R | B) = (8/12)·(4/11) = 8/33 ≈ 24.24%

So the probability the first is black and the second is red is about 24.24%.