Answer to Question #299864 in Statistics and Probability for Angie

Question #299864

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

1
Expert's answer
2022-02-22T12:42:22-0500

This is a binomial distribution with n=4,p=12.n=4,p=\frac{1}{2}.

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=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=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=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=4)=C44(12)0(12)0=116.P(T=4)=C_4^4(\frac{1}{2})^0(\frac{1}{2})^0=\frac{1}{16}.


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