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 :-
[tex]\text{Mean}:\mu=np\\\\\text{Variance}:\sigma^2=np(1-p)[/tex], where n is the total number of trials .
Given : A given binomial distribution has
[tex]\text{Mean}:\mu=np=4.......(1)\\\\\text{Variance}:\sigma^2=np(1-p)=2............(2)[/tex]
Now we substitute , the value of np from (1) in (2), we get
[tex]4(1-p)=2\\\\\Rightarrow\ 1-p=\dfrac{2}{4}\\\\\Rightarrow\ p=1-\dfrac{1}{2}\\\\\Rightarrow\ p=\dfrac{1}{2}=0.5[/tex]
Hence, the probability of success (p) = 0.5
