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} $
$=\frac{64}{125}+\frac{48}{125}=\frac{112}{125}=0.896$