Question

type the correct answer in the box. use numerals instead of words. use / for the fraction bar. a cooler contains 14 bottles of water and 10 bottles of lemonade. colleen randomly selects 2 bottles from the cooler without replacement. the probability, as a fraction in simplest terms, that colleen selected a bottle of water and then a bottle of lemonade is

Explanation:

Step1: Calculate total number of bottles

The total number of bottles initially is $14 + 10=24$ bottles.

Step2: Calculate probability of first - selecting a water bottle

The probability of selecting a water bottle first is $\frac{14}{24}=\frac{7}{12}$ since there are 14 water bottles out of 24 total bottles.

Step3: Calculate probability of second - selecting a lemonade bottle

After selecting a water bottle, there are $24 - 1=23$ bottles left, and 10 lemonade bottles. So the probability of selecting a lemonade bottle second is $\frac{10}{23}$.

Step4: Calculate the combined probability

Since these are dependent events, the probability of selecting a water bottle first and then a lemonade bottle is the product of the two probabilities. So $P=\frac{7}{12}\times\frac{10}{23}=\frac{7\times10}{12\times23}=\frac{70}{276}=\frac{35}{138}$.

Answer:

$\frac{35}{138}$