Answer:
[tex] P(X=3)[/tex]
And replacing we got:
[tex]P(X=3)=(4C3)(0.3)^3 (1-0.3)^{4-3}=0.0756[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of times that we select a blue ball", on this case we now that:
[tex]X \sim Binom(n=4, p=3/10)[/tex]
The probability is always the same since we replace the ball selected in each trial.
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=3)[/tex]
And replacing we got:
[tex]P(X=3)=(4C3)(0.3)^3 (1-0.3)^{4-3}=0.0756[/tex]
