Question

A given binomial distribution has mean-4 and variance-2. What is the probability of success? Explain your answer.

Answer 1

Answer: 0.5

Step-by-step explanation:

We know that the mean and variance of a binomial distribution with probability of success p is given by :-

$\text{Mean}:\mu=np\\\\\text{Variance}:\sigma^2=np(1-p)$, where n is the total number of trials .

Given : A given binomial distribution has

$\text{Mean}:\mu=np=4.......(1)\\\\\text{Variance}:\sigma^2=np(1-p)=2............(2)$

Now we substitute , the value of np from (1) in (2), we get

$4(1-p)=2\\\\\Rightarrow\ 1-p=\dfrac{2}{4}\\\\\Rightarrow\ p=1-\dfrac{1}{2}\\\\\Rightarrow\ p=\dfrac{1}{2}=0.5$

Hence, the probability of success (p) = 0.5