Four coins are tossed.Let T be the random variable representing the number of tails that occur.find the values of the random variable T
This is a binomial distribution with n=4,p=12.n=4,p=\frac{1}{2}.n=4,p=21.
P(T=0)=C40(12)0(12)4=116.P(T=0)=C_4^0(\frac{1}{2})^0(\frac{1}{2})^4=\frac{1}{16}.P(T=0)=C40(21)0(21)4=161.
P(T=1)=C41(12)1(12)3=14.P(T=1)=C_4^1(\frac{1}{2})^1(\frac{1}{2})^3=\frac{1}{4}.P(T=1)=C41(21)1(21)3=41.
P(T=2)=C42(12)2(12)2=38.P(T=2)=C_4^2(\frac{1}{2})^2(\frac{1}{2})^2=\frac{3}{8}.P(T=2)=C42(21)2(21)2=83.
P(T=3)=C43(12)0(12)1=14.P(T=3)=C_4^3(\frac{1}{2})^0(\frac{1}{2})^1=\frac{1}{4}.P(T=3)=C43(21)0(21)1=41.
P(T=4)=C44(12)0(12)0=116.P(T=4)=C_4^4(\frac{1}{2})^0(\frac{1}{2})^0=\frac{1}{16}.P(T=4)=C44(21)0(21)0=161.
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