Answer:
[tex]P(\text{Pizza}\ |\ \text{Female})=0.225[/tex]
Step-by-step explanation:
The two-way frequency table is attached below.
We have to calculate the probability of, a person chosen at random prefers pizza given that they are female, i.e [tex]P(\text{Pizza}\ |\ \text{female})[/tex]
This is a conditional probability.
We know that,
[tex]P(A\ |\ B)=\dfrac{P(A\ \cap\ B)}{P(B)}[/tex]
So,
[tex]P(\text{Pizza}\ |\ \text{Female})=\dfrac{P(\text{Pizza}\ \cap\ \text{Female)}}{P({\text{Female}})}[/tex]
From the table,
[tex]P(\text{Pizza}\ \cap\ \text{Female)}=\dfrac{119}{1000}[/tex]
[tex]P({\text{Female}})=\dfrac{530}{1000}[/tex]
Putting the values,
[tex]P(\text{Pizza}\ |\ \text{Female})=\dfrac{P(\text{Pizza}\ \cap\ \text{Female)}}{P({\text{Female}})}=\dfrac{\frac{119}{1000}}{\frac{530}{1000}}=0.225[/tex]
