Explanation

(c)
Given,$P(A) = 0.3,P(B) = 0.4,\ P(C) = 0.8,$
$P(A \cap B) = 0.08,\ P(A \cap C) = 0.28,$
$P(A \cap B \cap C) = 0.09$
$Since,\ P(A \cup B \cup C) \geq 0.75$
$\Rightarrow P(A) + P(B) + P(C) - P(A \cap C) - P(A \cap C)$
$- P(B \cap C) + P(A \cap B \cap C) \geq 0.75$
$\Rightarrow 0.3 + 0.4 + 0.8 - 0.08 - 0.28 - P(B \cap C) + 0.09 \geq 0.75$
$\Rightarrow P(B \cap C) \leq 0.48$
Also, $P(A \cup B \cup C) \leq 1$
$\Rightarrow 1.23 - P(B \cap C) \leq 1$
$\Rightarrow P(B \cap C) \geq 0.23$
$\therefore 0.23 \leq P(B \cap C) \leq 0.48$