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

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

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

$P(T=1)=C_4^1(\frac{1}{2})^1(\frac{1}{2})^3=\frac{1}{4}.$

$P(T=2)=C_4^2(\frac{1}{2})^2(\frac{1}{2})^2=\frac{3}{8}.$

$P(T=3)=C_4^3(\frac{1}{2})^0(\frac{1}{2})^1=\frac{1}{4}.$

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