Home
Class 12
MATHS
If P(B)=(3)/(4) P(A cap B cap overset(-)...

If P(B)`=(3)/(4)` P(A cap B cap overset(-)(c ))=(1)/(3)` and `P(overset(" "-)(A) cap B cap overset(-)(C ))=(1)/(3)`, then `P(B cap C)` is equal to

A

`(1)/(12)`

B

`(1)/(6)`

C

`(1)/(16)`

D

`(1)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `P(B)=(3)/(4),P(AnnBnnbarC)=(1)/(3)`

and `P(barAnnBnnbarC)=(1)/(3)`
which can be shown in Venn diagram.
`:. P(BnnC)=P(B)-{P(AnnBnnbarC+P(barAnnBnnbarC))}`
`=(3)/(4)-((1)/(3)+(1)/(3))=(3)/(4)-(2)/(3)=(1)/(12)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If n(A)=8 and n(A cap B)=2, then n((A cap B)' cap A) is equal to

If A and B are two events such that P(bar(A))= (3)/(10) and P (A capbar(B)) = (1)/(2) " then " P(A cap B) is . . . . . .

If A and B are two given sets then A cap (A capB)^(c) is equal to

If two events A and B are such that P(barA)=(3)/(10)" and "P( A cap bar B)=(1)/(2) then P(A cap B)=

The set (A cap B')cup (B cap C) equals

If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability of A and if P(A cap B)=(1)/(6), P(B cap C)=(1)/(4), P(A cap C)=(1)/(8), P(A cup B cup C)=(9)/(10),P(A cap B cap C)=(1)/(15) , then find P(A), P(B) and P(C ) ?

For any three sets A, B and C, (A-B)cap(B-C) is equal to