STEP - BY - STEP EXPLANATION
What to find?
p(male) x p(pass)
The type of event.
Given:
Total number of male =40+25 =65
Total number of pass =40 + 88 =128
Total number of students = 40 + 88 + 25 + 55 =208
Determine each probability using the formula below:
[tex]probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex][tex]P(male)=\frac{65}{208}[/tex][tex]P(pass)=\frac{128}{208}[/tex][tex]\begin{gathered} P(male)\times p(passed)=\frac{65}{208}\times\frac{128}{208} \\ \\ =\frac{8320}{43264} \\ \\ \approx0.192 \end{gathered}[/tex][tex]\begin{gathered} P(male\text{ and pass\rparen=}\frac{40}{208} \\ \\ \approx0.192 \end{gathered}[/tex]
The two results are independent.
ANSWER
Since p(male) x p(passed) =0.192 and P(male x passed) = 0.192, the two results are the same so the events are independent.
