Five hundred consumers were surveyed about a new brand of snack food, Crunchicle

Question

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

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?

    

Box 1: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity

Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity

Box 3: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity

Box 4: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity

18–24 25–34 35–55 55 and over Total Liked Crunchicles 5 19 19 78 121 Disliked Crunchicles 48 36 47 83 214 No Preference 45 30 54 36 165 Total 98 85 120 197 500

Explanation / Answer

Solution:-

1) The probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles is 0.0413.

Number of people who likes crunchicles = 121

Number of people who are 18–24 years of age and like crunchicles = 5

The probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles = 5/121 = 0.0413

2) The probability that the selected consumer dislikes Crunchicles is 0.428.

Number of people who disliked Crunchicles = 214

Total number of people = 500

The probability that the selected consumer dislikes Crunchicles = 214/500 = 0.428.

3) The probability that the selected consumer is 35–55 years old or likes Crunchicles is 0.444.

Number of people who liked Crunchicles = 121

Number of people who are 35 - 55 years of age = 120

Number of people who are 35-55 years of age or like crunchicles = 121 + 120 - 19

The probability that the selected consumer is 35–55 years old or likes Crunchicles = 222/500 = 0.444.

4) If the selected consumer is 70 years old, the probability that he/she likes Crunchicles is 0.3959.

Number of consumer who are 55 or older year old = 197

Number of people who are 55 or older year old and like crunchicles = 78

If the selected consumer is 70 years old, the probability that he/she likes Crunchicles = 78/197 = 0.3959

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