Answer: Choice A)
A and X are independent events
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Explanation:
If two events A and B are independent, then
P(A and B) = P(A)*P(B)
where the P stands for probability
In this case, X takes place of B, so
P(A and X) = P(A)*P(X)
There are 15 items that are in the "A" row and "X" column. This is out of 100 total. So
P(A and X) = 15/100 = 0.15
While
P(A) = 30/100 = 0.3
since there are 30 total for A out of 100 total overall
and
P(X) = 50/100 = 0.5
for similar reasons
So
P(A)*P(X) = 0.3*0.5 = 0.15
The fact we got the same result means that P(A and X) = P(A)*P(X) is a true equation. Therefore, events A and X are independent events.
