Question 1182451
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Use 12 as the denominator for each probability, since 12 is the least common multiple of 2, 3, and 4.<br>
Given: P(A) = 6/12; P(B) = 4/12; P(A∩B) = 3/12<br>
Then
P(A∩B') = P(A)-P(A∩B) = 6/12-3/12 = 3/12
P(A'∩B) = P(B)-P(A∩B) = 4/12-3/12 = 1/12<br>
P(AUB) = P(A)+P(B)-P(A∩B) = 6/12+4/12-3/12 = 7/12
P(A'∩B') = 1-P(AUB) = 1-7/12 = 5/12<br>
i) P(A|B) = P(A∩B)/P(A) = (3/12)/(6/12) = 3/6 = 1/2<br>
ii) P(B|A) = P(A∩B)/P(B) = (3/12)/(4/12) = 3/4<br>
iii) (from above) P(AUB) = 7/12<br>
iv) P(A'|B') = P(A'∩B')/P(B') = (5/12)/(1-4/12) = (5/12)/(8/12) = 5/8<br>