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A and B are two events such that odds odds against A are 2 : 1 odds in favour of `A cup B` are 3 : 1. If `x le P(B) le y`, then the ordered pair (x, y
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A and B are two events such that odds odds...
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A and B are two events such that odds odds against A are 2 : 1 odds in favour of A∪B are 3 : 1. If x≤P(B)≤y, then the ordered pair (x, y) is A. (5/12,3/4) B. (2/3,3/4) C. (1/3,3/4) D. none of these Select the correct answer from above options
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Correct Answer - A We have, P(A)= 1 3 andP(A∪B)= 3 4 ∴P(A∪B)=P(A)+P(B)-P(A∩B) ⇒ 3 4 = 1 3 +P(B)-P(A∩B) ⇒ 5 12 =P(B)-P(A∩B) ⇒P(B)= 5 12 +P(A∩B)⇒P(B)≥5/12 Again, P(B)= 5 12 +P(A∩B) ⇒P(B)≤5/12+P(A) [∵P(A∩B)≤P(A)] ⇒P(B)≤ 5 2 + 1 3 = 3 4 From (i) and (ii), we obtain 5/12≤P(B)≤3/4 Hence, x=5/12 andy=3/4
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