Question

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

Answer 1

Given:

The total number of people are T = 267.

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,

$\begin{gathered} P(t)=\frac{107}{267} \\ =0.4007 \end{gathered}$

(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.

$\begin{gathered} P(v)=\frac{109}{267} \\ =0.4082 \end{gathered}$

(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.

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

(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.

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

(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,

$\begin{gathered} P\text{ (s|C)=}\frac{P\text{ (s and c)}}{P\text{ (c)}} \\ =\frac{\frac{9}{267}}{\frac{52}{267}} \\ =\frac{9}{52} \\ \approx0.1731 \end{gathered}$

(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.

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

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