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# A die is thrown120 times and getting 1 or 5 is considered success. Find the mean,varianceof numberofsuccesses.

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• $P(X=r)=^nC_r.p^r.q^{n-r}$
This question is from Binomial distribution.
Let $X$=Distribution function which is no. of success.
$p=$ Probability of success=Probability of getting $1$ or $5=\large\frac{2}{6}=\frac{1}{3}$
$q=$ Probability of failure=$1=\large\frac{1}{3}=\frac{2}{3}$
$n=120$
$P(X=r)=^nC_r.p^r.q^{n-r}$
Mean of the distribution $=np=120\times\large\frac{1}{3}=$$40 Variance of the distribution =npq=120\times\large\frac{1}{3}$$\times\large\frac{2}{3}=\frac{80}{3}$
answered Jan 16, 2014
selected Jan 17, 2014 by pady_1