Explanation
Solution
1. Statement 1 ki jaanch:
Addition Rule ke hisaab se:
P(X∪Y)=P(X)+P(Y)−P(X∩Y)
Agar hum X=Aˉ aur Y=B rakhein:
P(Aˉ∪B)=P(Aˉ)+P(B)−P(Aˉ∩B)
Isliye, Statement 1 sahi hai.
2. Statement 2 ki jaanch:
Addition Rule se:
P(A∪Bˉ)=P(A)+P(Bˉ)−P(A∩Bˉ)
Lekin question mein diya hai: P(B)−P(A∩B), jo ki P(B∩Aˉ) ka formula hai.
Isliye, Statement 2 galat hai.
3. Statement 3 ki jaanch:
Conditional probability ke formula se:
P(A∣B)=P(B)P(A∩B)
Cross-multiply karne par:
P(A∩B)=P(B)⋅P(A∣B)
Isliye, Statement 3 sahi hai.
Correct Option: (b) 1 and 3 only