Probability: Is the manager telling the truth?

[sanctifier]

Homework Statement

The manager of a factory proclaims 99% of the products manufactured in his factory are unflawed. If we draw 50 products from 5000 products and find 2 of 50 are flawed, then how do we know the manage is telling the truth?

Homework Equations

Nothing special.

The Attempt at a Solution

Answer:

$\frac{{5000*0.99 \choose 48} {5000*0.01 \choose 2}}{ {5000 \choose 50}} \approx 0.0754$

Manager lied.

Is this correct? Thank you in advance!

 

[mfb]

You cannot conclude that the manager lied based on this result. You could have been unlucky with the 50 products. A probability of 7.5% is still reasonable and needs more tests before such a strong conclusion can be drawn.