If P (A) = 0.54, P(B) = 0.69 and P (A∩B) = 0.35 find P(AUB)
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P(AUB) = 0.88
Step-by-step explanation:
P(AUB) = P (A) + P(B) - P (A∩B)
P(AUB) = 0.54+0.69-0.35 = 0.88
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Q) If P (A) = 0.54, P(B) = 0.69 and P (A∩B) = 0.35 find P(AUB)
ANSWER:-
it is given that P(A)=0.54,P(B)=0.69,P(A∩B)=0.35
(i) We know that P (A∪B)=P(A)+P(B)−P(A∩B)
∴P(A∪B)=0.54+0.69−0.35=0.88
(ii) A ′ ∩B ′ =(A∪B) ′ , [by De Morgan's law]
∴P(A ′ ∩B ′ )=P(A∪B) ′ =1−P(A∪B)=1−0.88=0.12
(iii) P(A∩B) ′ =P(A)−P(A∩B)=0.54−0.35=0.19
(iv)We know that, P(B∩A )=P(B)−P(A∩B)
∴P(B∩A′ )=0.69−0.35=0.34
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