Answer:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]
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 can find this probability:
[tex] P(X \geq 1)[/tex]
And we can solve this probability like this:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
