Question

Two 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*?

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

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

What is the probability that the selected consumer dislikes

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

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

Answer #1

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

Three 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
2
4
3
5
14
Disliked Crunchicles
2
5
6
43
56
No Preference
60
71
27
72
230
Total
64
80
36
120
300
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