type the correct answer in the box. use numerals instead of words. use / for the fraction bar.\na cooler…

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

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

Answer

Explanation:

Step1: Calculate total initial bottles

$14 + 10 = 24$

Step2: Probability of first water bottle

$\frac{14}{24} = \frac{7}{12}$

Step3: Total bottles after first pick

$24 - 1 = 23$

Step4: Probability of second lemonade bottle

$\frac{10}{23}$

Step5: Multiply the two probabilities

$\frac{7}{12} \times \frac{10}{23} = \frac{70}{276}$

Step6: Simplify the fraction

$\frac{70 \div 2}{276 \div 2} = \frac{35}{138}$

Answer:

$\frac{35}{138}$