Sum

Solve the following:

If P(A ∩ B) = `1/2`, P(B ∩ C) = `1/3`, P(C ∩ A) = `1/6` then find P(A), P(B) and P(C)

Advertisement Remove all ads

#### Solution

Since A and B are independent events,

P(A ∩ B) = P(A) . P(B)

∴ P(A) P(B) = `1/2` ...(i)

B and C are independent events.

∴ P(B ∩ C) = P(B) . P(C)

∴ P(B) P(C) = `1/3` ...(ii)

A and C are independent events.

∴ P(A ∩ C) = P(A) . P(C)

∴ P(A) P(C) = `1/6` ...(iii)

Dividing (i) by (ii), we get

`("P"("A")"P"("B"))/("P"("B")"P"("C")) = (1/2)/(1/3)`

∴ P(A) = `3/2` P(C) ...(iv)

Substituting equation (iv) in (iii), we get

`3/2`P(C) . P(C) = `1/6`

∴ [P(C)]^{2} = `1/9`

∴ P(C) = `1/3`

Substituting P(C) = `1/3` in equation (ii), we get P(B) = 1

Substituting P(B) = 1 in equation (i), we get P(A) = `1/2`

Concept: Independent Events

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads