Question

You are sent to the local tea shop to pick up 12 drinks. You purchase 8 sweet teas and 4 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.

a) All of the 3 drinks picked are sweet teas.



b) Exactly one drink is sweetened.

Answer 1

a) The probability of picking a sweet tea on the first draw is 8/12. Since we did not replace the first tea, the probability of picking another sweet tea on the second draw is 7/11. Similarly, the probability of picking a sweet tea on the third draw is 6/10. Therefore, the probability of picking 3 sweet teas in a row is:

(8/12) * (7/11) * (6/10) = 0.2545 or 127/500

b) There are 3 ways to pick exactly one sweet tea: S U U, U S U, U U S, where S represents a sweet tea and U represents an unsweetened tea. The probability of picking a sweet tea on the first draw is 8/12, and the probability of picking an unsweetened tea is 4/12. Therefore, the probability of picking exactly one sweet tea is:

(8/12) * (4/11) * (3/10) + (4/12) * (8/11) * (3/10) + (4/12) * (3/11) * (8/10) = 0.4364 or 48/110