Home
Class 12
MATHS
Let A and B be the events such that P(...

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.

Text Solution

Verified by Experts

The correct Answer is:
(i) No (ii) No
P (not A or not B) `=P (bar(A) or bar(B))=P( bar(A) uu bar(B))`
`=P (bar(A nn B))=1- P (A nn B)`
`implies 1-P (A nn B)=1/4 implies P(A nn B)=3/4`.
(i) Since `P(A nn B) ne 0`, so A and B are not mutually exclusive.
(ii) `P(A)xxP(B)=(1/2xx7/12)=7/24 ne P(A nn B)`
`implies` A and B are not independent.
Promotional Banner

Similar Questions

Explore conceptually related problems

Events A and B are 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 independents?

Events A and B are such that P(A)=1/2,\ P(b)=7/(12) and P( not A or not )=1/4 . State whether A and B are independent?

If A and B are two 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 independent?

If P(A) = 1/2, P (B) = 7/12 and P ( not A or not B) =1/4 , State whether A and B are independent .

If A and B are events such that P(A)=(1)/(2), P(B) =(7)/(12) " and " P(A' uu B') =(1)/(4), then A and B are

Given that the events A and B are such that P" "(A)" "=1/2 , P(AnnB)=3/5 and P(B)" "=" "p . Find p if they are (i) mutually exclusive (ii) independent.

If A and B are two events such that P(A)=1/2, P(AuuB)=3/5 and P(B)=p , then find the value of p when: (i) A and B are mutually exclusive (ii) A and B are independent events.

If P(A) = 1/2, P(A cup B) = 3/5 and P (B) =q find the value of q is A and B are (i) Mutually exclusive (ii) independent events.

If the events A and B are mutually exclusive, then P( A/B) =

If A and B be two events such that P(A)=1//4, P(B)=1//3 and P(AuuB)=1//2 show that A and B are independent events.