Question

According to a recent​ study, 14% of u.s. drivers are uninsured. a random sample of seven drivers was selected. what is the probability that none of these drivers are​ uninsured?

Answer 1

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:

$\mathbf{P(X=x) =_{n}^{x}\textrm{C}*p^{x}*q^{(n-x)}}$

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 = $1-0.14 = 0.86$

$_{n}^{x}\textrm{C}$ is the combination of choosing x items from a total of n items

Substituting the values we get

$\mathbf{P(X=x) =\frac{n!}{x!*(n-x)!}*p^{x}*q^{(n-x)}}$

$\mathbf{P(X=x)=\frac{7!}{0!*(7-0)!}*0.14^{0}*0.84^{(7-0)}}$

$\mathbf{P(X=x)= 1*1*0.84^{(7-0)}}$

$\mathbf{P(X=x)= 0.347927822}$