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

Answer:

C

Step-by-step 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

$P_1=\dfrac{7}{14}=\dfrac{1}{2}$

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

$P_2=\dfrac{6}{13}$

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

$P=P_1\cdot P_2=\dfrac{1}{2}\cdot \dfrac{6}{13}=\dfrac{3}{13}$