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Question

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.

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Solution

Let the probability of getting a tail in the biased coin be x.

P(T)=x

P(H)=3x

For a biased coin, P(T)+P(H)=1

x+3x=1

4x=1

x=14

P(T)=14 and P(H)=34

When the coin is tossed twice, the sample space is {HH,TT,HT,TH}.

Let X be the random variable representing the number of tails.
P(X=0)=P(notail)=P(H)×P(H)=34×34=916

P(X=1)=P(onetail)=P(HT)+P(TH)

=3414+1434

=316+316

=38

P(X=2)=P(twotails)=P(TT)=14×14=116

Therefore, the required probability distribution is as follows.

955679_423157_ans_e829e1444fe4448db4e3512efd3fdf02.png

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