If A and B are independent events., where P(A) = 0.3, P(B) = 0.6, then

1.	If A and B are independent events., where P(A) = 0.3, P(B) = 0.6, then find: (i) P(A ∩ B) (ii) P(A ∪ \(\bar{B}\)) (iii) P(A ∪ B) (iv) P(\(\bar{A}\) ∩ \(\bar{B}\))
Answer» Given P(A) = 0.3 P(B) = 0.6 (i) P(A ∩ B) = P(A) × P(B) = 0.3 × 0.6 = 0.18 (ii) P(A ∪ \(\bar{B}\)) = 0.3 – 0.18 = 0.12 (iii) P(A ∪ B) = p(A) + P(B) – P(A ∩ B) = 0.3 + 0.6 – 0.18 = 0.90 – 0.18 (iv) P(\(\bar{A}\) ∩ \(\bar{B}\)) = [1 – P(A)] [1 – P(B)] = [1 – 0.3] [1 – 0.6] = 0. 7 × 0.4 = 0.28

If A and B are independent events., where P(A) = 0.3, P(B) = 0.6, then find: (i) P(A ∩ B) (ii) P(A ∪ \(\bar{B}\)) (iii) P(A ∪ B) (iv) P(\(\bar{A}\) ∩ \(\bar{B}\))

Answer»

Given

P(A) = 0.3

P(B) = 0.6

(i) P(A ∩ B) = P(A) × P(B)

= 0.3 × 0.6

= 0.18

(ii) P(A ∪ \(\bar{B}\))

= 0.3 – 0.18

= 0.12

(iii) P(A ∪ B) = p(A) + P(B) – P(A ∩ B)

= 0.3 + 0.6 – 0.18

= 0.90 – 0.18

(iv) P(\(\bar{A}\) ∩ \(\bar{B}\)) = [1 – P(A)] [1 – P(B)]

= [1 – 0.3] [1 – 0.6]

= 0. 7 × 0.4

= 0.28

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If A and B are independent events., where P(A) = 0.3, P(B) = 0.6, then find: (i) P(A ∩ B) (ii) P(A ∪ \(\bar{B}\)) (iii) P(A ∪ B) (iv) P(\(\bar{A}\) ∩ \(\bar{B}\))

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