Question

7) A cooler contains ten bottles of sports drink: three lemon-lime flavored, four orange flavored, and three 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

Explanation:

The probability of randomly selecting a lemon-lime flavored drink twice in a row can be calculated using the concept of conditional probability. First, let's determine the probability of selecting a lemon-lime flavored drink on the first attempt. Out of the ten bottles in the cooler, three are lemon-lime flavored. Therefore, the probability of selecting a lemon-lime flavored drink on the first attempt is 3/10. After returning the first bottle to the cooler and mixing up the bottles, there are still ten bottles in total. However, since you already selected a lemon-lime flavored drink, there are now only two lemon-lime flavored drinks left in the cooler. Therefore, the probability of selecting another lemon-lime flavored drink on the second attempt is 2/10. To find the probability of both events occurring (selecting a lemon-lime flavored drink twice in a row), we multiply the probabilities of each event together. So, the probability of randomly selecting a lemon-lime flavored drink twice in a row is (3/10) * (2/10) = 6/100 = 3/50. Therefore, the reason you obtained two lemon-lime drinks in a row is that there was a 3/50 probability of this occurrence happening based on the initial distribution of drinks in the cooler.