ANSWER
[tex]P(A \cap B')=0.36[/tex]
EXPLANATION
If event A and event B are independent, then
[tex]P(A \cap B)= P(A ) \times P(B)[/tex]
otherwise A and B are dependent events.
We were given that,
[tex]P(A) = 0.4[/tex]
and
[tex]P(B) = 0.1[/tex]
and we were asked to evaluate
[tex]P(A \cap B') [/tex]
Since A and B are independent,
[tex]P(A \cap B') = P(A ) \times P(B') [/tex]
Recall that,
[tex]P(B') = 1 - P( B) [/tex]
This implies that,
[tex]P(A \cap B') = P(A ) \times (1 - P(B) )[/tex]
We now substitute the above values to obtain,
[tex]P(A \cap B') = 0.4 \times (1 - 0.1 )[/tex]
[tex]P(A \cap B') = 0.4 \times 0.9[/tex]
[tex]P(A \cap B') = 0.36[/tex]
Therefore the correct answer is C.
