A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Answer

N/a

Explanation

Let `X` be a random variable which represents the number of tails in two throws of a biased coin. Therefore the possible values of `X` are 0,1 or 2.
Since coin is biased in which the possibility of getting head is three times are possbility of getting tail.
`:.P({H})=3/4` and `P({T})=1/4`
`P(X=0)=P({"HH"})=(3/4)^(2)=9/16`
`P(X=1)=P` (a tail and a head)
`=P({HT,TH}=P({HT})+P{(TH})`
`=P({H})P({T})+P({T})P({H})`
`=3/4xx1/4+1/4xx3/4=3/16+3/16=6/16=3/8`
`P(X=2)=P` (two tails) `=P({"TT"})=P({T}).P({T})`
`=(1/4)^(2)=1/16`
Therefore required probability distribution is: