1. ## Probability question -

If 85 percent of the autos arriving at the Lincoln Tunnel have either New York or New Jersey license plates, what is the probability that, of the next 20 autos, 2 or fewer (i.e., 0, 1, 2) will bear license plates from states other than New York or New Jersey?

Here is the answer I came up with...
0.667

The answer I came up with is incorrect. I used the 85% divided by 20 then multiplied the answer by 2

Thanks,

2. Hi!

Let $B=\mbox{ "Less than 2/20 cars have different types of plates" }$

What you have is a binomial distribution with success if a car has a different type of plate, and failure if it has a New York och New Jerser plate.

$X=\mbox{ the number of cars with other types of plates }$

With $p_{success}=\frac{15}{100}$ and $p_{failure}=\frac{85}{100}$ , we get

$P(B)=P(X=0)+P(X=1)+P(X=2)=\displaystyle\sum_{k=0}^ {2}\binom{20}{k}\left(\frac{15}{100}\right)^{k}\le ft(\frac{85}{100}\right)^{20-k} \approx 0.405$

3. Thank you so much. I understand now the failure vs. success problem. I tried it with another set of numbers and I got the right answer.

Thank you so much.