Question

The Florida Tourist Commission selected a random sample of 200 people that attended one or more concerts during the first weekend in April of 2010. The survey revealed that 120 concert goers went to Orlampa Skydome and 100 went to the Bithlo Megaplax. Calculate the probability that a selected concert goer during the same weekend next year will go to either the Orlampa Skydome OR the Bithlo Megaplax?

Answer 1

0.8 or 80%

Explanation:

Let A and B be the events

A: “The concert goer went to Orlampa Skydome”

B: “The concert goer went to the Bithlo Megaplax”

Then the probability P(A) that a concert goer went to Orlampa Skydome is

P(A) = 120/200 = 0.6

Similarly,

P(B) = 100/200 = 0.5

We are looking for P(A∪B), the probability that a concert goer went to Orlampa Skydome OR the Bithlo Megaplax.

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

but P(A∩B) is the likelihood that a concert goer went to Orlampa Skydome AND the Bithlo Megaplax.

Since the events are independent,

P(A∩B) = P(A)P(B) = 0.6*0.5 = 0.3

and

P(A∪B) = 0.6 +0.5 - 0.3 = 0.8 or 80%