Given:
The two way table.
To find:
The conditional probability of P(Drive to school | Senior).
Solution:
The conditional probability is defined as:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Using this formula, we get
[tex]P(\text{Drive to school }|\text{ Senior})=\dfrac{P(\text{Drive to school and senior})}{P(\text{Senior})}[/tex] ...(i)
From the given two way table, we get
Drive to school and senior = 25
Senior = 25+5+5
= 35
Total = 2+25+3+13+20+2+25+5+5
= 100
Now,
[tex]P(\text{Drive to school and senior})=\dfrac{25}{100}[/tex]
[tex]P(\text{Senior})=\dfrac{35}{100}[/tex]
Substituting these values in (i), we get
[tex]P(\text{Drive to school }|\text{ Senior})=\dfrac{\dfrac{25}{100}}{\dfrac{35}{100}}[/tex]
[tex]P(\text{Drive to school }|\text{ Senior})=\dfrac{25}{35}[/tex]
[tex]P(\text{Drive to school }|\text{ Senior})=0.7142857[/tex]
[tex]P(\text{Drive to school }|\text{ Senior})\approx 0.71[/tex]
Therefore, the required conditional probability is 0.71.
