in Education by
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

1 Answer

0 votes
by
 
Best answer
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

Related questions

0 votes
    If X and Y are two events such that PX/Y)= 1 2 ,P(Y/X)= 1 3 and P(X∩Y) 1 6 . Then, which of the ... 1 6 D. X and Y are not independent Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
0 votes
    Let A and B be two events such that P(A∪B)=P(A∩B) . Then, Statement-1: P(A∩ ˉ B )=P( ˉ A ∩B)=0 ... -1 is False, Statement-2 is True. Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
    Let X and Y be two events such that P(X/Y) = \(\frac{1}{2}\) , P(Y/X) =\(\frac{1}{3}\) and P(X∩Y) =\( ... (d) P(XC∩Y) = \(\frac{1}{3}\) Select the correct answer from above options...
asked Nov 19, 2021 in Education by JackTerrance
0 votes
0 votes
    Statement-1: Let n≤3 and A1,A2,..,An be n independent events such that P(Ak)= 1 k+1 for 1≤k≤n, then P( ... False, Statement-2 is True. Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
0 votes
0 votes
    If A and B are two events such that P ( A ) = 1 2 P and P ( B ) = 2 3 P , then which of the following is ... ( ¯¯¯ A ∩ B ) ≤ 1 2 1 Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
0 votes
    If A and B are two events associated with a random experiment such that P(A)=0.3,P(B)=0.2 and P(A∩B)=0.1, ... the value of P(A∪B) is . Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
    A and B are two events such that P(A∪B)= 3 4 ,P(A)= 1 3 ,P( ˉ A ∩B)= A. 5 12 B. 3 8 C. 5 8 D. 1 4 Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
0 votes
    If A and B are two independent events such that P( ˉ A )= 7 10 ,P( ˉ B )=α andP(A∪B)= 8 10 , then α, is ... 5/7 C. 1 D. none of these Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
0 votes
    If P(A)= 2 3 ,P(B)= 1 2 and P(A∪B)= 5 6 , then events A and B are A. mutually exclusive B. ... C. independent D. dependent only on A Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
    You are given that A and B are two events such that P(B)= 3/5, P(A | B) = 1/2 and P(A ∪ B) = 4/5, then P(A ... /10 B. 1/5 C. 1/2 D. 3/5 Select the correct answer from above options...
asked Nov 20, 2021 in Education by JackTerrance
0 votes
    State True or False for the statements: If A, B and C are three independent events such that P(A) = P(B) = P( ... C occur) = 3p2 - 2p3 Select the correct answer from above options...
asked Nov 19, 2021 in Education by JackTerrance
0 votes
    If A and B are two independent events such that P(A)= 1 2 and P(B)= 1 5 , then which of the following is incorrect ... ˉ A ∪ ˉ B )=1/2 Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
...