What is the probability of this happening ?

Question

A cooler contains fourteen bottles of sports drink: 4 lemon lime flavored, 5 orange flavored, and 5 fruit punch flavored. You randomly grab a bottle. Then you return the bottle to the cooler, mix up the bottles, and randomly select another bottle. Both times you get a lemon lime drink.

Answer 1

For the 1st pick, the probability of getting lemon lime is 4/14 or 2/7.

Because the 1st pick is returned to the sample space prior to the 2nd pick, the probability of getting lemon lime on the 2nd pick is also 2/7.

The probability that BOTH happened is 2/7 • 2/7 = 4/49

Answer 2

The distinction between with replacement or without is important. In this case the first drink is chosen and replaced.

We have two events and the total probability can be found by multiplying the two probabilities.

So what is the probability that the first drink is Lemon Line, P(LL)? That's quite easy to get. If you don't know I can help.

Now what is the probability that the second drink is LL? Is it any different from the first?

Hopefully that gets you on your way. Let us know.