Answer:
P(A)= 0.606 and P(B)= 0.237
Step-by-step explanation:
Since A and B are independent
P(A ∩ B) = P(A) * P(B) → P(B) = P(A ∩ B) / P(A)
and also
P(A ∪ B)= P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = P(A) + P(A ∩ B) / P(A) - P(A ∩ B)
[P(A ∪ B) + P(A ∩ B) ]* P(A) = P(A)² + P(A ∩ B)
P(A)² - [P(A ∪ B) + P(A ∩ B) ]* P(A) + P(A ∩ B) = 0
P(A)² - [ 0.626+0.144] * P(A) + 0.144 =0
P(A)² - 0.77* P(A) + 0.144 =0
thus
P(A)₁= 0.606 or P(A)₂= 0.1647
for P(A)₁→ P(B)₁ = P(A ∩ B) / P(A)₁ = 0.144/0.606 = 0.237
thus P(A)₁ > P(B)₁ → correct
for P(A)₂→ P(B)₂ = P(A ∩ B) / P(A)₂ = 0.144/0.1647= 0.8743
thus P(A)₂ < P(B)₂ → incorrect
therefore
P(A)= 0.606 and P(B)= 0.237
