Question

Two hundred consumers are 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	14	6	15	39	74
Disliked Crunchicles	7	6	3	27	43
No Preference	12	15	5	51	83
Total	33	27	23	117	200

One consumer from the survey is selected at random. Leave all answers in a reduced fraction.

1. What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles?
   
      
   
2. What is the probability that the selected consumer dislikes Crunchicles?
   
      
   
3. What is the probability that the selected consumer is 35–55 years old or likes Crunchicles?
   
      
   
4. If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?

Answer 1

The probabilities are obtained by dividing the respective values by the total of 200

For example probability that a consumer Liked Crunchicles and of 18–24 years of age = 14/200

Likewise all the probabilities are calculated and shown in the below table

	18–24	25–34	35–55	55 and over	Total
Liked Crunchicles	14/200	6/200	15/200	39/200	74/200
Disliked Crunchicles	7/200	6/200	3/200	27/200	43/200
No Preference	12/200	15/200	5/200	51/200	83/200
Total	33/200	27/200	23/200	117/200	1

Question (1)

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

Here we should use condiional probability

P(A | B) read as P(A given B) = P(A B) / P(B)

Here A is the consumer is 18-24 years of age

B is consumer dislikes Crunchicies

P ( consumer is 18-24 years of age | consumer dislikes Crunchicies) = (7/200) / (43/200)

= 7/43

Question (2)

Probability that the selected consumer dislikes Crunchicles = 43/200

Question (3)

Probability that the selected consumer is 35–55 years old or likes Crunchicles

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

Here A is consumer is 35-55 years old and B is consumer likes crunchicies

Probability that the selected consumer is 35–55 years old or likes Crunchicles = (23/200) + (74/200) - (15/200)

= 41/100

Question (4)

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

Here we should use condiional probability

P(A | B) read as P(A given B) = P(A B) / P(B)

Here A is the consumer likes Crunchicies

B is consumer is 70 years old. Consumer will fall into 55 and over category

P ( consumer likes Crunchicies | consumer is 70 years old) = (39/200) / (117/200)

= 39 / 117

= 1/3