A snack cracker company surveyed 1000 people, in different age groups, to determ

Question

A snack cracker company surveyed 1000 people, in different age groups, to determine their favorite cracker. a. What is the probability (represented as a percent) that a randomly selected participant was 20 years old or older? b. 152 of the participants under 20 years old chose cracker A as their favorite. Calculate the probability that a participant chose cracker A or was under 20 years old. c. What is the probability that a participant did not choose cracker A and was 20 or over years old? Show how you used a complement to answer this problem.

Explanation / Answer

(a)

Out of 1000 people surveyed, 750 are 20 year or older so requried probability is

P(20 year or older) = 750/ 1000 = 0.75 = 75%

(b)

From the table we have

P(under 20) = 250/1000

P(cracker A) = 371/1000

P(cracker A|under 20) = 152 /250

So

P(cracker A and under 20) = P(cracker A|under 20) P(under 20) = (152/250) * (250/1000) = 152/1000

So requried probability is

P(cracker A or under 20) =P(cracker A) +P(under 20) -P(cracker A and under 20) =(371/1000) + (250/1000) - (152/1000) = 0.469

(c)

By the complement rule we have

P(not cracker A and not under 20) = 1 - P(cracker A or under 20) = 1 - 0.469 = 0.531

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