Given P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.24.Find (i) P(A ∪ B

1.	Given P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.24.Find (i) P(A ∪ B) (ii) P(\(\bar{A}\) ∩ B) (iii) P(A ∩ \(\bar{B}\)) (iv) P(\(\bar{A}\) ∪ \(\bar{B}\))(v) P(\(\bar{A}\) ∩ \(\bar{B}\))
Answer» (i) P(A) = 0.5, P(B) = 0.6, P(A ∩ B) = 0.24 P(A ∪ B) = P(A) + P(B) – P(A ∩ B) (i.e.,) P(A ∪ B) = 0.5 + 0.6 – 0.24 = 1.1 – 0.24 = 0.86 ∴ P(A ∪ B) = 0.86 (ii) P(\(\bar{A}\) ∩ B) = P(B) – P(A ∩ B) = 0.6 – 0.24 = 0.36 (iii) P(A ∩ \(\bar{B}\)) = P(A) – P(A ∩ B) = 0.5 – 0.24 = 0.26 (iv) P(\(\bar{A}\) ∪ \(\bar{B}\)) = P {(A ∩ B)’} = 1 – P(A ∩ B) = 1 – 0.24 = 0.76 (v) P(\(\bar{A}\) ∩ \(\bar{B}\)) = P{A ∪ B)’} = 1 – P(A ∪ B) = 1 – 0.86 = 0.14.

Given P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.24.Find (i) P(A ∪ B) (ii) P(\(\bar{A}\) ∩ B) (iii) P(A ∩ \(\bar{B}\)) (iv) P(\(\bar{A}\) ∪ \(\bar{B}\))(v) P(\(\bar{A}\) ∩ \(\bar{B}\))

Answer»

(i) P(A) = 0.5, P(B) = 0.6, P(A ∩ B) = 0.24

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

(i.e.,) P(A ∪ B) = 0.5 + 0.6 – 0.24

= 1.1 – 0.24 = 0.86

∴ P(A ∪ B) = 0.86

(ii) P(\(\bar{A}\) ∩ B) = P(B) – P(A ∩ B)

= 0.6 – 0.24 = 0.36

(iii) P(A ∩ \(\bar{B}\)) = P(A) – P(A ∩ B)

= 0.5 – 0.24 = 0.26

(iv) P(\(\bar{A}\) ∪ \(\bar{B}\)) = P {(A ∩ B)’} = 1 – P(A ∩ B)

= 1 – 0.24 = 0.76

(v) P(\(\bar{A}\) ∩ \(\bar{B}\)) = P{A ∪ B)’} = 1 – P(A ∪ B)

= 1 – 0.86 = 0.14.

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Given P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.24.Find (i) P(A ∪ B) (ii) P(\(\bar{A}\) ∩ B) (iii) P(A ∩ \(\bar{B}\)) (iv) P(\(\bar{A}\) ∪ \(\bar{B}\))(v) P(\(\bar{A}\) ∩ \(\bar{B}\))

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