Question

If P(A)=0.1, P(B)=0.2 and P(AUB)=0.25, then find P(B/A’) and
P(A’/B’).

Answer 1

Explanation:

$P(A)=0.1, P(B)=0.2 \: , P(AUB)=0.25 \\\\\\P(A \cap \: B) =P(A) + P(B) - P(AUB) \\\\ = 0.1 + 0.2 - 0.25 \\\\ = 0.05 \\\\ P(A ’) = 1 -P(A ) \\\\ = 1 - 0.1 \\\\ = 0.9\\\\ P(A ’\cap \: B) = P(B) +P(A \cap \: B) \\\\ = 0.2 + 0.05\\\\ = 0.25 \\\\ P(B/A’) = \frac{P(A ’\cap \: B)}{P(A ’)} \\\\ = \frac{0.25}{0.9} \\\\ = 0.28\\ \\ P(B’) = 1 -P(B) \\\\ = 1 - 0.2 \\\\ = 0.8 \\\\ P(A’ \cap \: B’) =P(A \cup \: B)’ \\\\ = 1 - P(A\cup \: B) \\\\ =1 - 0.25 \\\\ = 0.75 \\\\ P(A’/B’) = \frac{P(A’ \cap \: B’)}{P(B’)} \\\\ = \frac{0.75}{0.8} \\\\ = 0.94$