Question

1. P(adult and vanilla)2. P(chocolate/adult)3. P(adult/chocolate)4. P(not vanilla/teen)5. P(teen/not vanilla)6. P(neither/teen or adult)7. P(teen or adult/neither)Answer the following problems about two way frequency tables and make sure to reduce your fraction.

Answer 1

From the given table, the total number of people, T=269.

1)

The number of adults who like vanila, N=54.

So, P(adult and vanilla) can be found as,

`P\mleft(adult\text{ and vanilla}\mright)=(N)/(T)=(54)/(269)`

2)

P(chocolate/adult) can be found as,

`P\mleft(chocolate/adult\mright)=\frac{P(\text{choclate and adult)}}{P(\text{adult)}}=((55)/(269))/((119)/(269))=(55)/(269)`

3)

`P\mleft(adult/chocolate\mright)=\frac{P(\text{choclate and adult)}}{P(\text{chocolate)}}=((55)/(269))/((107)/(269))=(55)/(107)`

4)

`P\mleft(notvanilla/teen\mright)=\frac{P(not\text{ vanilla and t}een)}{P(\text{teen)}}=((12+45)/(2))/((73)/(269))=(57)/(73)`

5)

`P\mleft(teen/notvanilla\mright)=\frac{P(\text{teen and not vanilla)}}{P(\text{not vanilla)}}=((12+45)/(269))/((269-92)/(269))=(57)/(177)`

6)

`P\mleft(neither/teenoradult\mright)=\frac{P(\text{neither and teen or adult)}}{P(\text{teen or adult)}}=((45+10)/(269))/((73+119)/(269))=(55)/(192)`

7)

`P\mleft(teenoradult/neither\mright)=\frac{P(\text{teen or adult and neither)}}{P(\text{neither)}}=((45+10)/(269))/((70)/(269))=(55)/(70)=(11)/(14)`