Maharashtra State BoardHSC Science (General) 11th
Advertisement Remove all ads

Solve the following: If P(A ∩ B) = 12, P(B ∩ C) = 13, P(C ∩ A) = 16 then find P(A), P(B) and P(C) - Mathematics and Statistics

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

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (4) | Page 213
Advertisement Remove all ads

Video TutorialsVIEW ALL [2]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×