Question

Hi, can you help me answer this question please, thank you:)

Answer 1

Given:

The total number of people are T = 267.

Step-by-step explanation:

(a)

Determine the total number of teens.

`\begin{gathered} t=39+43+25 \\ =107 \end{gathered}`

The probability for the person to be a teen is,

`\begin{gathered} P(t)=(107)/(267) \\ =0.4007 \end{gathered}`

(b)

Determine the number of people like the vanilla.

`\begin{gathered} v=22+43+44 \\ =109 \end{gathered}`

Determine the propability for the person selected likes the Vanilla.

`\begin{gathered} P(v)=(109)/(267) \\ =0.4082 \end{gathered}`

(c)

Determine the number of people that are teen or likes the vanailla.

`\begin{gathered} v\text{ OR t=}22+43+44+39+25 \\ =173 \end{gathered}`

Determine the probability for a selected person is a teen or like the vanilla.

`\begin{gathered} P\text{ (v or t)=}(173)/(267) \\ =0.6479 \end{gathered}`

(d)

The number of person that is teen and likes strawberry best are 25.

Determine the probability for selected person is teen and likes strawberry best.

`\begin{gathered} P\text{ (t and s)=}(25)/(267) \\ =0.0936 \end{gathered}`

(e)

Determine the number of persons that are children.

`\begin{gathered} C=21+22+9 \\ =52 \end{gathered}`

Determine the number person that are children and likes strawberry best.

`\text{ C and s=}9`

So probability for the person likes the strawbwerry given that person is children is,

`\begin{gathered} P\textC)=\frac{P\text{ (s and c)}}{P\text{ (c)}} \\ =((9)/(267))/((52)/(267)) \\ =(9)/(52) \\ \approx0.1731 \end{gathered}`

(f)

The number of persons who likes the strawberry best is,

`\begin{gathered} s=9+25+25 \\ =62 \end{gathered}`

Determine the probability for person is teen given that person likes strawberry best.

`\begin{gathered} P\text{ (}t|s\text{)}=\frac{P\text{ (t and s)}}{P(s)} \\ =((25)/(267))/((62)/(267)) \\ =(25)/(62) \\ =0.4032 \end{gathered}`

Answer:

Is a teen: 0.4007

Likes vanilla the best: 0.4082

Is a teen or likes the Vanilla the best: 0.6479

Is a teen and likes the strawberry best: 0.0936

Likes strawberry the best GIVEN the person is child: 0.1732

Is a teen GIVEN that person likes the strawberry best: 0.4032