1) Since this is a Conditional Probability, we can write out the following formula for that:
[tex]P(pass|male)=\frac{P(pass\text{ }\cap\text{ male)}}{P(\text{male)}}[/tex]
2) Now, in the table we can see that the subspace for those who passed is the sum of all who passed:
28 +12 = 40
The Subspace for the students is:
21 +49 = 70
And now we can plug into that formula checking in the table:
[tex]\begin{gathered} P(pass|male)=\frac{P(pass\text{ }\cap\text{ male)}}{P(\text{male)}} \\ P(pass|male)=\frac{\frac{12}{40}}{\frac{40}{70}}=\frac{12}{40}\cdot\frac{40}{70}=\frac{6}{35}\text{ or 0.17}1 \end{gathered}[/tex]
2.2) The Probability of being approved:
[tex]P(\text{pass)}=\frac{40}{70}=\frac{4}{7}=0.571[/tex]
We can check whether two events are independent if we can state that
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