Question

A two-way frequency table is shown below displaying the relationship between age and preferred cola beverage. We took a sample of 100 people and recorded the following results:

Cola Rootbeer Dr. Fizz TOTAL
10-25 10 5 20 35
26-40 15 10 10 35
41-55 20 10 0 30
TOTAL 45 25 30 100


What is the probability (rounded to the nearest whole percent) that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz?


55%

35%

60%

0%

Answer 1

60%

Explanation:

The table with proper formatting is attached below.

We have to find the probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz.

Total number of people = 100

People in range 41 - 55 = 30

People who prefer Dr. Fizz = 30

People in range of 41 - 55 and prefer Dr. Fizz = 0

The general formula of probability in case of OR of two events is:

P ( A or B ) = P(A) + P(B) - P( A and B)

So for the given case we can write:

P (Person is in 41-55 range OR prefer Dr. Fizz) = P (Person is in 41 - 55 range) + P(Prefers Dr. Fizz) - P(Is in 41-55 range And prefers Dr. Fizz)

P (Person is in 41-55 range OR prefer Dr. Fizz) = 30/100 + 30/100 - 0/100

= 60/100

= 60%

Thus there is a 60% probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz