Question

The probability that an event does not happen in one trial is $0.8$ The probability that the event happens atmost once in three trials is

• A. 0.896
• B. 0.791
• C. 0.642
• D. 0.592

Answer 1

Answer: (A)

Here $p=0.2,q=0.8,n=3,r=0,1$
From binomial distribution,
$P(X=r)={}^n{C}_r{P}^r{q}^{n-r}$
$p(X=r)=P(X=0)+P(X=1)$
$={}^3{C}_0(0.2{)}^0(0.8{)}^{3-0}+{}^3{C}_1(0.2{)}^1(0.8{)}^{3-1}$
$=\frac{3!}{0!3!}\times 1\times {\left(\frac{8}{10}\right)}^3+\frac{3!}{1!2!}\left(\frac{2}{10}\right){\left(\frac{8}{10}\right)}^2$
$=1\times 1\times {\left(\frac{8}{10}\right)}^3+\frac{3\times 2}{2\times 1}\times \frac{2}{10}\times \frac{8}{10}\times \frac{8}{10}$
$=\frac{64}{125}+\frac{48}{125}=\frac{112}{125}=0.896$