To solve problems about probabilities that are expressed as 'A given B' where A and B are events, we need to use the Conditional Probability, which formula is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
This is read as 'probability of A given B'
In the case of our problem, A is male and B is not a bachelor's
Notice that the total amount of recipients is 2501
Therefore, the probability intersection is
[tex]P(A\cap B)=\frac{224+245}{Total}[/tex]
Where total refers to the total amount of recipients, then
[tex]P(A\cap B)=\frac{469}{2501}\approx0.1875[/tex]
Know, as for the probability of event B,
[tex]P(B)=\frac{224+245+387+322}{Total}=\frac{1178}{2501}\approx0.471[/tex]
Finally, the probability we are looking for is:
[tex]P(A|B)=\frac{\frac{469}{2501}}{\frac{1178}{2501}}=\frac{469}{1178}\approx0.3981[/tex]
