Question

In a binomial distribution consisting of 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. The parameter p of the distribution is

• A. $1/3$
• B. $1/4$
• C. $1/5$
• D. $1/6$

Answer 1

Answer: (C)

$1/5$

In a binomial distribution consisting of 5 independent trials, n = 5
The probability of 1 and 2 successes are 0.4096 and 0.2048 respectively.
${}^5{C}_1{p}^1{(1-p)}^{5-1}=0.4096$ ${}^5{C}_2{p}^2{(1-p)}^{5-2}=0.2048$
$5p{(1-p)}^4=0.4096$ _____ (1) $10p^2{(1-p)}^3=0.2048$ ______ (2)
Divide equation (1) by (2), we get
$\frac{(1-p)}{2p}=2$

$5p=1$

$p=\frac{1}{5}$