Answer :

(i) Here

P(A) = , P(B) =

P(A ∩ B) = P(A ∪ B) = ?

We know that

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= +

= = =

(ii) Here, P(A) = 0.35

P(B) = ?

P(A ∩ B) = 0.25

P(A ∪ B) = 0.6

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ 0.6 = 0.35 + P(B) – 0.25

⇒ 0.85 – 0.35 = P(B)

⇒ P(B) = 0.5

(iii) Here P(A) = 0.5

P(B) = 0.35

P(A ∩ B) = ?

P(A ∪ B) = 0.7

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

0.7 = 0.5 + 0.35 – P(A ∩ B)

0.7 = 0.85 - P(A ∩ B)

P(A ∩ B) = 0.85 – 0.7 = 0.15

P(A ∩ B) = 0.15.

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