If A and B be two events and 2P(B) = P(A) = 6/13 and P(A/B) = 1/3 then

1.	If A and B be two events and 2P(B) = P(A) = 6/13 and P(A/B) = 1/3 then find P(A ∪ B).
Answer» Given, 2P(B) = P(A) = 6/13 2P(B) = 6/13; P(B) = 3/13 again, P(A) = 6/13 According to question, P(A/B) = 1/3; P(A ∩ B)/P(B) = 1/3; P(A ∩ B)/(3/13) = 1/3 P(A ∩ B) = (1/3) x (3/13) P(A ∩ B) = 1/3 P(A ∪ B) = p(A) + P(B) - P(A ∩B) = (6/13) + (3/13) - (1/13) = (6 + 3)/13 - (1/13) = (9/13) - (1/13) = 8/3

If A and B be two events and 2P(B) = P(A) = 6/13 and P(A/B) = 1/3 then find P(A ∪ B).

Answer»

Given, 2P(B) = P(A) = 6/13

2P(B) = 6/13; P(B) = 3/13 again, P(A) = 6/13

According to question,

P(A/B) = 1/3; P(A ∩ B)/P(B) = 1/3; P(A ∩ B)/(3/13) = 1/3

P(A ∩ B) = (1/3) x (3/13)

P(A ∩ B) = 1/3

P(A ∪ B) = p(A) + P(B) - P(A ∩B)

= (6/13) + (3/13) - (1/13)

= (6 + 3)/13 - (1/13)

= (9/13) - (1/13)

= 8/3