A pencil box contains 6 green and 3 yellow crayons. Two crayons are taken out together (simultaneously) at random. What is the probability that one crayon is green and the other is yellow?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{2}\)
Taking two crayons together is a selection, so outcomes are counted with combinations. One green and one yellow means choosing 1 of the 6 green crayons and 1 of the 3 yellow crayons, so the two counts are multiplied.
Total crayons \(=6+3=9\); ways to take 2 \(\displaystyle ={}^{9}C_2=\frac{9\times8}{2}=36\)
Ways to take 1 green and 1 yellow \(={}^{6}C_1\times{}^{3}C_1=6\times3=18\)
Probability \(\displaystyle =\frac{18}{36}=\frac{1}{2}\)