Question

The table below shows the soft drinks preferences of people in three age groups cola under 21 years of age between 21 and 40 over 40 years of age 40 35 20 root beer lemon-lime 25 20 20 30 30 35 Round all answers to 3 decimals. A) What is the probability that a randomly selected person prefers root beer or is over 40 years of age? B) What is the probability that a randomly selected person is between 21 and 40 years of age ? C) What is the probability that a randomly selected cola drinker is under 21 years of age (that is, find the probability of being under 21 given the person is a cola drinker)? D) What is the probability that a randomly selected person is under 21 years of age and prefers root boor?

Answer 1

cola 85 under 21 21 and 40 over 40 years Total 85 root beer lemon lime Total 40 25 20 35 20 30 20 30 35 95 75 85 85 255

a. Probability a person perfers root beer or is over 40 years of age?

P(Prefers root beer or Over 40 years of age) = P(Prefers root beer) + P(Over 40 years of age) - P(Prefers root beer and Over 40 years of age)

P(Prefers root beer) = (no. of people of perfer root beer) / Total people = 75/255 = 0.2941

P (Over 40 years of age) = (no. of people Over 40 years of age) / Total people = 85/255 = 0.3333

P(Prefers root beer and Over 40 years of age) = (no. of people refers root beer and Over 40 years of ag) / Total people = 30/255 = 0.1176

P(Prefers root beer or Over 40 years of age) = 0.2941 + 0.3333 - 0.1176 = 0.5098

b. Probability a selected person is between 21 and 40 years of age
P( between 21 and 40 years of age) = (no. of people between 21 and 40 years of age) / Total people = 85/255 =0.3333

c. Probability that selected cola drinker is under 21 years of age?
Probability of being under 21 given the person is a cola drinker?

P(Under 21 of age | A cola drinker) = P(Under 21 of age and a cola drinker) / P( a cola drinker)

P(Under 21 of age and a cola drinker) = no of Under 21 of age and a cola drinker / Total people = 40/255 = 0.1569

P( a cola drinker) = no of person who drink cola/ Total people = 95/255 = 0.3725

P(Under 21 of age and a cola drinker) = 0.1569/ 0.3725 = 0.4212

d. Probability is under 21 years and perfer root beer

P(under 21 years and perfer root beer)= no of people under 21 years and prefer root beer/ total people = 25/255 = 0.0980