Ask a Question

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 ?

in Education by
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 ? A. P(A∪B)=3/5 B. P(A/B)=1/2 C. P(A/A∪B)=5/6 D. P(A∩B/ ˉ A ∪ ˉ B )=1/2 Select the correct answer from above options

1 Answer

0 votes
by
 
Best answer
Correct Answer - D Since A and B are independent events. Therefore, P(A∩B)=P(A)P(B)= 1 2 × 1 5 = 1 10 and, P(A/B)=P(A)= 1 2 So, alternative (b) is correct. Now, P(A∪B)=P(A)+P(B)-P(A∩B)= 1 2 + 1 5 - 1 10 = 3 5 So, alternative (a) is correct. Now, P(A/A∪B)= P[A∩(A∪B)] P(A∪B) = P(A) P(A∪B) = 1/2 3/5 = 5 6 So, alternative (c ) is correct. and, P(A∩B/ ˉ A ∪ ˉ B )=P( ¯ A∪B )=0

Related questions

0 votes
Q: If A and B are two events such that `P(A)=(1)/(2)` and `P(B)=(2)/(3)`, then which of the following is incorrect ?
    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
Q: If A and B are two independent events such that `P(overline(A) cap B)=2//15 " and " P(A cap overline(B))=1//6`, then P(B), is
    If A and B are two independent events such that P( ˉ A ∩B)=2/15 and P(A∩ ˉ B )=1/6, then P(B), is A. 1 5 or ... or, 1 6 D. 5 6 or, 1 5 Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
0 votes
Q: Statement-1 : If A and B are two events such that P(A)=1, then A and B are independent. Statement-2: A and B are two independent events iff `P(A cap B
    Statement-1 : If A and B are two events such that P(A)=1, then A and B are independent. Statement-2: A ... False, Statement-2 is True. Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
Q: If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P (At least two of A, B, C occur) = 3p^2 – 2p^3
    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
Q: If `A and B` are two independent events such that `P(B) = 2/7, , P(A uu B) = 0.8` then `P(A)=`
    If AandB are two independent events such that P(B)= 2 7 ,,P(A∪B)=0.8 then P(A)= A. 0.1 B. 0.2 C. 0.3 D. 0.4 Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
Q: 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) equals
    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
Q: If A and B are two independent events such that `P(overline(A))=(7)/(10), P(overline(B))=alpha " and" P(A cup B)=(8)/(10)`, then `alpha`, is
    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
Q: If `A and B` are independent events of a random experiment such that `P(A nn B) = 1/6 and P( overlineA nn overlineB)=1/3` then `P(A)=`
    If AandB are independent events of a random experiment such that P(A∩B)= 1 6 andP( ˉ A ∩ ˉ B )= 1 3 then P(A)= A. ... 1 3 C. 1 6 D. 2 3 Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
Q: If A and B are two events such that P(A) = 1/2, P(B) = 1/3 , P(A/B) = 1/4 , then P(A' ∩ B' ) equals A. 1/12 B. 3/4 C. 1/4 D. 3/16
    If A and B are two events such that P(A) = 1/2, P(B) = 1/3 , P(A/B) = 1/4 , then P(A' ∩ B' ) equals A. 1/12 B. 3/4 C. 1/4 D. 3/16 Select the correct answer from above options...
asked Nov 20, 2021 in Education by JackTerrance
0 votes
Q: 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
    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 ... 3,3/4) D. none of these Select the correct answer from above options...
asked Nov 16, 2021 in Education by JackTerrance
0 votes
Q: If A and B are two events associated with a random experiment such that `P(A)=0.3,P(B)=0.2" and "P(AcapB)=0.1,` then the value of `P(A∪B)` is ….
    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
Q: If E1 and E2 are the two events such that P (E1) = 1/4, P (E2) = 1/3 and P (E1 U E2) = 1/2, show that E1 and E2 are independent events.
    If E1 and E2 are the two events such that P (E1) = 1/4, P (E2) = 1/3 and P (E1 U E2) = 1/2, show that E1 and E2 are independent events. Select the correct answer from above options...
asked Nov 21, 2021 in Education by JackTerrance
0 votes
Q: Let A and B be two independent events. Statement-1: If P(A)=0.3 and `P(A cup overline(B))=0.8`, then `P(B)=(2)/(7)` Statement-2: For any event `E, P(o
    Let A and B be two independent events. Statement-1: If P(A)=0.3 and P(A∪ ˉ B )=0.8, then P(B)= 2 ... -1 is False, Statement-2 is True. Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
Q: If X and Y are two events such that `PX//Y)=(1)/(2), P(Y//X)=(1)/(3)` and `P(XcapY)(1)/(6)`. Then, which of the following is/are correct ?
    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

© Copyright 2018-2023 www.Blogmepost.com. All rights reserved. Developed by Blogmepost.

...