Question

A cooler contains eleven bottles of sports drink: four lemon-lime flavored, four orange flavored, and three fruit-punch flavored. You randomly grab a bottle. It is a lemon-lime or an orange.

Answer 1

To find the probability we need to use the addition rule:

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

where A is the event "the flavor is lemon lime" and B is the event "the flavor is orange". Since the events are mutually exclusive the formula above reduces to:

$P(A\cup B)=P(A)+P(B)$

Then the probability we are looking for is:

$P(A\cup B)=\frac{4}{11}+\frac{4}{11}=\frac{8}{11}$

therefore the probability is 8/11.