To determine [tex]\( P(A \cap B) \)[/tex], we can use the definition of conditional probability. The conditional probability [tex]\( P(A \mid B) \)[/tex] is given by:
[tex]\[
P(A \mid B) = \frac{P(A \cap B)}{P(B)}
\][/tex]
We are given [tex]\( P(A \mid B) = 0.25 \)[/tex] and [tex]\( P(B) = 0.4 \)[/tex]. We need to find [tex]\( P(A \cap B) \)[/tex].
Rearranging the formula to solve for [tex]\( P(A \cap B) \)[/tex]:
[tex]\[
P(A \cap B) = P(A \mid B) \times P(B)
\][/tex]
Substitute the given values:
[tex]\[
P(A \cap B) = 0.25 \times 0.4
\][/tex]
Now, perform the multiplication:
[tex]\[
P(A \cap B) = 0.1
\][/tex]
Thus, the probability [tex]\( P(A \cap B) \)[/tex] is [tex]\( 0.1 \)[/tex].
Therefore, the correct answer is:
C. 0.1
