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Five 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 39 66 10 86 201
Disliked Crunchicles 27 19 38 95 179
No Preference 24 37 35 24 120
Total 90 122 83 205 500


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 they dislike Crunchicles?

Respuesta :

Answer:

The probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.

Step-by-step explanation:

The age groups and preferences are given as follows:

                                     18 - 24     25 - 34       35 - 55     55 and over      Total

Liked Crunchicles           39             66              10                  86                201

Disliked Crunchicles       27              19             38                  95                179

No Preference                 24             37             35                  24                120

Total                                 90           122             83                205               500

One consumer from the survey is selected at random.

Compute the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles as follows:

[tex]P(18-24|DC)=\frac{P(18-24\cap DC)}{P(DC)}[/tex]

                        [tex]=\frac{n(18-24\cap DC)}{n(DC)}\\\\=\frac{27}{179}\\\\=0.15084\\\\\approx 0.151[/tex]

Thus, the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.