A bag contains 5 red and 4 blue balls. Two balls are drawn together (simultaneously) at random from the bag. What is the probability that one ball is red and the other is blue?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{5}{9}\)
Drawing two balls together is a selection, so outcomes are counted with combinations. One red and one blue means choosing 1 of the 5 red balls and 1 of the 4 blue balls, so the two counts are multiplied.
Total balls \(=5+4=9\); ways to draw 2 \(\displaystyle ={}^{9}C_2=\frac{9\times8}{2}=36\)
Ways to draw 1 red and 1 blue \(={}^{5}C_1\times{}^{4}C_1=5\times4=20\)
Probability \(\displaystyle =\frac{20}{36}=\frac{5}{9}\)