Answer
Since P(female) x P(fail) = 0.262 and P(female and fail) = 0.262, the two results are equal so the event are independent.
Explanation
Given:
Total number of students = 30 + 109 + 70 + 39 = 248
Total number of male = 30 + 70 = 100
Total number of female = 109 + 39 = 148
Total number of pass = 30 + 109 = 138
Total number of fail = 70 + 39 = 109
Hence, P(female) x P(fail) is
[tex]P(female)\times P(fail)=\frac{148}{248}\times\frac{109}{248}=\frac{4033}{15376}=0.262[/tex]
The P(female and fail) is
[tex]P(female\text{ }and\text{ }fail)=\frac{148}{248}\times\frac{109}{248}=\frac{4033}{15376}=0.262[/tex]
Since P(female) x P(fail) = 0.262 and P(female and fail) = 0.262, the two results are equal so the event are independent.
