Answer:
Cross probability
Step-by-step explanation:
The type of probabilities remains to be determined. That is the question itself. The same problem is found in the book "Understanding basic statistics 7th edition of Brase".
I will assume that the three probabilities to find are:
a) p (woman asked for a raise)
b) p (received raise | asked for one)
c) p (received raise and asked for one)
So,
a) p(woman asked for a raise)
It is given in the statement, so it is simple statistics:
![P_{WomA} =25%](https://tex.z-dn.net/?f=P_%7BWomA%7D%20%3D25%25)
b) p(received raise | asked for one)
It is also found in the statement, however, now the formula would be given by:
<em>p(received raise | asked for one) = p(received raise and asked for one) / p(asked for one)</em>
![P_{WomB}=46%](https://tex.z-dn.net/?f=P_%7BWomB%7D%3D46%25)
c) p(received raise and asked for one)
For this case the formula is given differently and it is necessary to re-adjust formula B, as follows:
<em>p(received raise and asked for one) = p(received raise | asked for one) * p(asked for one)</em>
So,
![P_{WomC} = 0.46*0.25 = 11.5%](https://tex.z-dn.net/?f=P_%7BWomC%7D%20%3D%200.46%2A0.25%20%3D%2011.5%25)
p(received raise and asked for one) = 11.5%