Question

1) A cooler contains fourteen bottles of sports drink: seven lemon-lime flavored and seven orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. What is the probability that you and your friend both get lemon-lime?

A) 1:4
B) '1:14
C) 3:13
D) 12:121

Answer 1

C

Explanation:

A cooler contains 14 bottles of sports drink:

• 7 lemon-lime flavored
• 7 orange flavored.

The probability that the first bottle chosen will be lemon-lime is

`P_1=(7)/(14)=(1)/(2)`

Then

a cooler contains 13 bottles of sports drink:

• 6 lemon-lime flavored
• 7 orange flavored.

The probability that the second bottle chosen will be lemon-lime is

`P_2=(6)/(13)`

Hence, the probability that you and your friend both get lemon-lime bottles is

`P=P_1\cdot P_2=(1)/(2)\cdot (6)/(13)=(3)/(13)`