Answer: The probability that none of the drivers are uninsured is 0.3479 or 34.79%.
We can answer this question as follows:
We use the binomial distribution formula in order to find the probability.
The formula is as follows:
[tex]\mathbf{P(X=x) =_{n}^{x}\textrm{C}*p^{x}*q^{(n-x)}}[/tex]
where
n is the total number of trials = 7
x is the number of successes among the trials = 0
p refers to the probability of success = 0.14
q refers to the probability of failure = 1-p = [tex]1-0.14 = 0.86[/tex]
[tex]_{n}^{x}\textrm{C}[/tex] is the combination of choosing x items from a total of n items
Substituting the values we get
[tex]\mathbf{P(X=x) =\frac{n!}{x!*(n-x)!}*p^{x}*q^{(n-x)}}[/tex]
[tex]\mathbf{P(X=x)=\frac{7!}{0!*(7-0)!}*0.14^{0}*0.84^{(7-0)}}[/tex]
[tex]\mathbf{P(X=x)= 1*1*0.84^{(7-0)}}[/tex]
[tex]\mathbf{P(X=x)= 0.347927822}[/tex]
