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NeX [460]
3 years ago
7

A survey of 249 people asks about their favorite flavor of ice cream. The results of this survey, broken down by the age group o

f the respondent and their favorite flavor, are as follows:
Chocolate Vanilla Strawberry
Children 40 10 44
Teens 34 10 38
Adults 17 43 13
If one person is chosen at random, find the probability that the person:______.
a) is an adult.
b) likes chocolate the best.
c) is an adult OR likes vanilla the best.
d) is a child AND likes vanilla the best.
e) likes strawberry the best, GIVEN that the person is a child.
f) is a child, GIVEN that the person likes strawberry the best.
Mathematics
1 answer:
Tpy6a [65]3 years ago
4 0

Answer:

a) P(Adult)=\frac{73}{249}=0.2932=29.32%

b) P(Chocolate)=\frac{91}{249}=0.3655=36.55%

c) P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%

d) P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%

e) P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%

f) P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the number of adults in the survey and divide them into the number of people in the survey by using the following formula>

P=\frac{desired}{possible}

In this case we have a total of 17+43+13 adults which gives us 73 adults and a total of 249 people surveyed so we get:

P(Adults)=\frac{73}{249}=0.2932=29.32%

b)

The same principle works for part b

there are: 40+34+17=91 people who likes chocolate ice cream the best so the probability is:

P(Chocolate)=\frac{91}{249}=0.3655=36.55%

c)

when it comes to the or statement, we can use the following formula:

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

In this case:

P(Adult)=\frac{73}{249}

P(Vanilla)=\frac{10+10+43}{249}=\frac{63}{249}

P(AdultandVanilla)=\frac{43}{249}

so:

P(AdultorVanilla)=\frac{73}{249}+\frac{63}{249}-\frac{43}{249}

P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%

d)

Is a child and likes vanilla the best.

In the table we can see that 10 children like vanilla so the probability is:

P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%

e)

Likes strawberry the best, GIVEN that the person is a child.

In this case we can make use of the following formula:

P(B/A)=\frac{P(AandB)}{P(A)}

so we can get the desired probabilities. First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

P(childrenandstrawberry)=\frac{44}{249}

Then, we know there are 40+10+44=94 children, so the probability for the person being a child is:

P(Child)=\frac{94}{249}

Therefore:

P(Strawberry/Child)=\frac{\frac{44}{249}}{\frac{94}{249}}

P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%

f)

The same works for the probability of the person being a child given that the person likes strawberry the best.

First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

P(childrenandstrawberry)=\frac{44}{249}

Then, we know there are 44+38+13 persons like strawberry, so the probability for the person liking strawberry is:

P(Child)=\frac{95}{249}

Therefore:

P(Child/Strawberry)=\frac{\frac{44}{249}}{\frac{95}{249}}

P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%

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