Question

# Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups...

Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

18–24 25–34 35–55 55 and over Total
Liked Crunchicles 4 5 3 4 16
Disliked Crunchicles 7 22 22 36 87
No Preference 27 19 10 41 97
Total 38 46 35 81 200

One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.

What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles?

What is the probability that the selected consumer dislikes Crunchicles?

What is the probability that the selected consumer is 35–55 years old or likes Crunchicles?

If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?

Solution(a)
We need to calculate
P(Consumer is 18-24 years of age Given that he/she dislikes Crunchicles), here we will use Conditional probability
P(Consumer is 18-24 years of age Given that he/she dislikes Crunchicles) = P(Age is 18 -24 Years and Dislikes crunchicles)/P(Dislikes Crunchicles) = (7/200)/(87/200) = 7/87
Solution(b)
P(Consumer dislikes crunchicles) = No. of Consumer likes crunchicles/ Total No. of consumers = 87/200
Solution(c)
P(Selected consumer is 35-55 or Likes Crunchicles) = P(Selected Consumer is 35-55) + P(Likes Crunchicles) - P(consumer is 35-55 and likes crunchicles) = (35/200) + (16/200) - (3/200) = 48/200 = 6/25
Solution(d)
P(Likes crunchicles and Selected customer is 70 Years) = (Total No. of consumer like crunchy and 70 years old)/(Toal consumers) = 4/200 = 1/50