An urn contains four black and eight white balls. Three balls are drawn from the urn without replacement. Three events are defined on this experiment. A: Exactly one black ball is drawn. B.: All balls are drawn are of the same color. C: Third drawn ball is black. Match the entries of column I with none, one or more entries of column II. Column I, Column II The events `Aa n dB` are, p. mutually exclusive The events `Ba n dC` are, q. independent The events `Ca n dA` are, r. neither independent nor mutually exclusive The events `A ,Ba n dC` are, s. exhaustive

Answer

`a to p ; b to r ; c to q ; d to p `

Explanation

`atop,btor,ctoq,d to p.`
`P(A)=(""^(4)C_(1)""^(8)C_(2))/(""^(12)C_(3))=(4+56)/(220)=(60)/(220)=3/11`
`P(C) =P(WBBorBWBorWWBorBBB)`
`=8/12xx4/11xx3/10xx4/12xx8/11xx3/10xx8/12xx7/11xx4/10xx4/12xx3/11xx2/10`
`=(96+96+224+24)/(12xx110)=(440)/(12xx110)=1/3`
`AnnB=phiimpliesAand B` are mutually exclusive
`P(BnnC)=P(BBB)=(4xx3xx2)/(12xx110)=1/55`
Also, `P(B)P(C)=3/11xx1/3=1/11`
Hence, B and C aer neither independent nor matually exclusive.
`P(CnnA)=P(WWB)(8xx7xx4)/(12xx11xx10)=(28)/(3xx55)`
`P(C)P(A)=1/3xx112/220=(28)/(3xx55)`
Thus, C and A are independent.
Also, A,B,C are mutually exclusive as A and B are mutually exclusive.