Help with Probability question. (1 Viewer)

[Metho NoX]

Hello, I am not sure about this probability question.

The probability of three(3) new cars passing a quality control check are as follows:

P(3 passing) = 1/16
P(2 passing) = 7/16
P(1 passing) = 3/16
P(0 passing) = 5/16

Find the probability that at least one car will fail the check.

I got the answer 11/16 by doing this;

P(at least 1 failing) = 1 - P(0 passing)

But the answers says 15/16. Im not sure if I did this correct.

 

[PoLaRbEaR]

3 cars are pass the quality control check...this means that the answer is asking what is the probability that all 3 cars do not pass..
If 2 cars pass, then 1 fails;
if 1 car passes, then 2 fail; and
if 0 cars pass, then 3 fail

Therefore probability of at least 1 car failing is:
P(2 passing) + P(1 passing) +P(0 passing)
= 7/16 + 3/16 + 5/16
=15/16

OR

P(at least 1 failing) = 1 - P(3 passing)
=1 - 1/16
=15/16

 

[Lexicographer]

Ah! So the confusion lies not in the mathematics, but in the wording of the question!

 

[Metho NoX]

Thanks PoLaRbEaR, I hate these sorts of questions that require thinking.