Question

A large cooler contains the following drinks: 7 lemonades, 15 Sprites, 12 Cokes, and 9 root beers. You randomly pick two cans, one at a time (without replacement). Compute the following probabilities.

1. What is the probability that you get one can of Coke and one can of Sprite?
2. What is the probability that you get two drinks of the same type?

Answer 1

Answer :

P(One can of Coke and one of Sprite) = 0.20

P(two drinks) = 456 / 1722 = 0.26

Explaination :

For problem 1. P(of getting a Coke) = 12/42

P(getting Sprite) = 15/42.

Now for getting both Sprite and Coke you will multiply the probabilities and then multiply them with 2 because you may choose Coke in first try and Sprite in second or the other way around.

P(One can of Coke and one of Sprite) = 2 * 12/42 * 15/42 = 360 / 1764 = 0.20

P(two drink of the same type) = P(two Cokes) + P(two Sprite) + P(two root beer) + P(two lemonades)

P(two drink of the same type) =

12 * 11 / 42 * 41 + 15 * 14 / 42 * 41 +

9 * 8 / 42 * 41 + 7 * 6 / 42 * 41

P( two drinks) = 132 / 1722 + 210 / 1722 + 72 / 1722 + 42 / 1722

P(two drinks) = 456 / 1722 = 0.26