# Probability of passing inspection

• Dec 18th 2008, 11:19 AM
stella09
Probability of passing inspection
Okay here it is:

In a southern statek, it was revealed that 5% of all automobiles in the state did not pass inspection. Of the next ten automobiles entering the inspection station,
a. what is the probability that none will pass inspection?
b. the probability that all will pass?
c. the probability that exactly 2 will not pass?
d. the probability that more than 3 will not pass?
e. the probaility that fewer than two will not pass?

Thanks to anyone who provides help!
• Dec 18th 2008, 12:12 PM
JD-Styles
This is a binomial distribution. Let X be the number of trucks that do NOT pass inspection. Then for ten trucks we have:

$P(X=x)=\begin{pmatrix} 10 \\ x \end{pmatrix} (0.05)^x(0.95)^{10-x}$

a) We need to find P(X=10):

$P(X=10)=\begin{pmatrix} 10 \\ 10 \end{pmatrix} (0.05)^{10}(0.95)^{10-10}$

$P(X=10)=9.77 \times 10^{-14}$

b and c are pretty much the same, just set X=0 and X=2, respectively.

d) This one's a little different. We need to find P(X>3). This is equivalent to $1-P(X \le 3)$. The latter is easier to calculate so let's do that one.

$P(X>3)=1-P(X\le 3)$

$P(X>3)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)$

From here just plug in the appropriate values in the formula and you'll get your answer.

e is pretty similar to d, just find P(X<2)=P(X=0)+P(X=1)