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A bag contains a fair coin X and a two h...

A bag contains a fair coin X and a two headed coin Y. A coin is selected at random and tossed twice.
(i) If heads appears both times find the probability that the coin is two headed.
(ii) If tails appears both times, find the probability that the coin is two headed.

Text Solution

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Lets represent the data by tree diagram

We wish to find P(Y/HH) and P(Y//TT)
HH appears along the top path bottom path.
`P(HH)=1/2.(1)/(4)+(1)/(2).1=1/8+1/2=5/8`
`P(YcapHH)=(1)/(2).1=1/2`
And also
(i) `P(Y//HH)=(P(YcapHH))/(P(HH))=(1/2)/(5/8)=1/2.(8)/(5)=4/5`
(ii) As `P(Ycap"TT")=0`
`=P(Y//"TT")=(P(Ycap"TT"))/(P("TT"))=0{P("TT")ne0}`
Obviously if tails appears, it could not be a two headed coin.
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