Question

Find the P( the recipient is male, given that the degree is not bachlors)

Answer 1

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:

`P(A|B)=(P(A\cap B))/(P(B))`

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

`P(A\cap B)=(224+245)/(Total)`

Where total refers to the total amount of recipients, then

`P(A\cap B)=(469)/(2501)\approx0.1875`

Know, as for the probability of event B,

`P(B)=(224+245+387+322)/(Total)=(1178)/(2501)\approx0.471`

Finally, the probability we are looking for is:

`P(A|B)=((469)/(2501))/((1178)/(2501))=(469)/(1178)\approx0.3981`