Question

The probability that an event A occurs in a single trial of an experiment is $0.3$. Six independent trials of the experiment are performed. What is the variance of probability distribution of occurrence of event A?

• A. $12.6$
• B. $0.18$
• C. $1.26$
• D. $1.8$

Answer 1

The correct option is C $1.26$

X	0	1	2	3	4	5	6
P(X)	${}^6{C}_0\left({0.7}^6\right)\left({0.3}^0\right)$	${}^6{C}_1\left({0.7}^5\right)\left({0.3}^1\right)$	${}^6{C}_2\left({0.7}^4\right)\left({0.3}^2\right)$	${}^6{C}_3\left({0.7}^3\right)\left({0.3}^3\right)$	${}^6{C}_4\left({0.7}^2\right)\left({0.3}^4\right)$	${}^6{C}_5\left({0.7}^1\right)\left({0.3}^5\right)$	${}^6{C}_6\left({0.7}^0\right)\left({0.3}^6\right)$

$\mu =\sum X_{i}P\left(X_i\right)$

$={\sum }_0^{6}i{\times }^6{C}_i\left({0.7}^{6-i}\right)\left({0.3}^i\right)$

$=1.8$

$variance=\sum X_i^{2}P\left(X_i\right)-{\mu }^2$

$=4.5-{1.8}^2$

$=1.26$

Hence the answer is option (C).