in Education by
Let A and B be the events such that P(A) = 1/2, P(B) = 7/12 and P(not A or not B) = 1/4. State whether A and B are (i) mutually exclusive (ii) independent Select the correct answer from above options

1 Answer

0 votes
by
 
Best answer
Given: A and B are the events such that P(A) = 1 2 and P(B) = 7 12 and P(not A or not B) = 1 4 To Find: (i) If A and B are mutually exclusive Since P(not A or not B) = 1 4 i.e., P( ¯ A ∪ ¯ B ) = 1 4 we know that , P( ¯ A ∪ ¯ B ) ) = P(A ∩ B)' = 1 - P(A ∩ B) = 0 But here P(A ∩ B) ≠ 0 Therefore , A and B are not mutually exclusive. (ii) If A and B are independent The condition for two events to be independent is given by P(E1 ∩ E2) = P(E1) x P(E2) = 1 2 × 7 12 = 7 24 Equation 2 Since Equation 1 ≠ Equation 2 ⇒ A and B are not independent

Related questions

0 votes
    Let A and B be the events such that P (A) = 1/2, P (B) = 7/12 and P (not A or not B) = ... (i) mutually exclusive, (ii) independent. Select the correct answer from above options...
asked Nov 21, 2021 in Education by JackTerrance
0 votes
    Let A and B be the events such that P (A) = 7/12, P (B) = 9/13 and P (A ∩ B) = 4/13. Find (i) P (A/B) ... P (A U B) (iv) P(bar B/bar A) Select the correct answer from above options...
asked Nov 22, 2021 in Education by JackTerrance
0 votes
    Let A and B be the events such that P(A) = 7/13, P(B) = 9/13 and P(A ∩ B) = 4/13. Find (i) P(A ... (iv) P(\(\overline B/\overline A\)) Select the correct answer from above options...
asked Nov 17, 2021 in Education by JackTerrance
0 votes
0 votes
    Let A and B be two events such that p( ˉ A ∪B)= 1 6 ,p(A∩B)= 1 4 and p( ˉ A )= ... independent D. equally likely and mutually exclusive Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
    Let A and B be two events such that p( ˉ A ∪B)= 1 6 ,p(A∩B)= 1 4 and p( ˉ A )= 1 ... independent D. equally likely but not independent Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
0 votes
    Let A and B be the events such that P (A) = 3/10, P (B) = 1/2 and P (B/A) = 2/5. Find (i) P (A ∩ B) (ii) P (A U B) (iii) P (A/B). Select the correct answer from above options...
asked Nov 22, 2021 in Education by JackTerrance
0 votes
    Let A and B be the events such that P(A) = 3/10,P(B) = 1/2 and P(B/A) = 2/5. Find (i) P(A ∩ B) (ii) P(A ∪ B) (iii) P(A / B) Select the correct answer from above options...
asked Nov 17, 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 A and B be the events such that P (A) = 5/11, P (B) = 6/11, P (A U B) = 7/11. Find (i) P (A ∩ B) ... ) P (B/A) (iv) P(bar A/bar B) Select the correct answer from above options...
asked Nov 22, 2021 in Education by JackTerrance
0 votes
    Let A and B be the events such that P(A) = 5/11,P(B) = 6/11 and P(A ∪ B) = 7/11. Find (i) P(A ∩ B) (ii) ... B / A) (iv) P( ¯ A / ¯ B ) Select the correct answer from above options...
asked Nov 17, 2021 in Education by JackTerrance
0 votes
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
    Let A and B be two events such that P(A) = 3/8, P(B) = 5/8 and P(A ∪ B) = 3/4. Then P(A | B).P(A′ | B) ... .2/5 B. 3/8 C. 3/20 D. 6/25 Select the correct answer from above options...
asked Nov 20, 2021 in Education by JackTerrance
0 votes
    Let A, B and C be three events such that P(A)=0.3,P(B)=0.4,P(C)=0.8,P(A∩B)=0.08,P(A∩C)=0.28,P( ... 23≤P(B∩C)≤0.48 D. 0.23≤P(B∩C)≤0.48 Select the correct answer from above options...
asked Nov 15, 2021 in Education by JackTerrance
...