Consider the experiment of throwing a die if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event the coin shows a tail given that at least one die shows as three.

Answer

N/a

Explanation

Sample space is
`{{:((3,1)","(3,2)","(3,3)","(3,4)","(3,5)","(3,6)),((6,1)","(6,2)","(6,3)","(6,4)","(6,5)","(6,6)),((1,H)","(1,T)","(2H)","(2,T)","(4,H)","(4,T)),((5,H)","(5,T)):}}`
`impliesn(S)=20`
Let `E=` event of getting tail and
`F=` event of getting 3 on a dice
`E={(1,T),(2,T),(4,T),(5,T)},`
`implies n(E)=4`
`F={(3,1),(3,2),(3,3),(3,4),(3,5),`
`(3,6),(6,3)}`
`implies n(F)=7`
`impliesEnnF=phi` because there is no common point.
`:.P(E)=(n(E))/(n(S))=4/20=1/5`
`P(F)=(n(F))/(n(S))=7/20`
and `P(EnnF)=(n(EnnF))/(n(S))=0/20=0`
Therefore, required probability
`=P(E/F)=(P(EnnF))/(P(F))=3/(7/20)=0`