Suppose the following holds:

• [math]A [/math] is independent of both [math]B [/math] and [math]C[/math]
• [math]\operatorname{P}(B \cup C ) = 0.7 [/math]
• [math]\operatorname{P}(A) = 0.5 [/math], [math]\operatorname{P}(B) = 0.5 [/math] and [math]\operatorname{P}(C) = 0.3 [/math]
• [math]\operatorname{P}(A \cup B \cup C) = 1[/math]

Determine [math]\operatorname{P}(A \cap B \cap C) [/math].

1. 0
2. 0.1
3. 0.15
4. 0.2
5. 0.3