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Answer 1

Answer:

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

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=41

∴P(T)=41 and P(H)=43

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)=43×43=169

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

=43⋅41+41⋅