An IRS agent has 19 tax returns on her desk of which 14 were

An IRS agent has 19 tax returns on her desk, of which 14 were filed using the short form (1040A). She randomly chooses 8 returns to audit. Determine the probability of the following:

At least 6 were filed using the short form.

This is what I got:

P(at least 6) = P(6)+ P(7)+ P(8)

P(k) = C(8,k) p^k (1p)^(8k)

p=14/19=.7368

1-p=.2632

=(8,6)(.7368)^6(.2632)^2+(8,7)(.7368)^7(.2632)+(8,8)(.7368)^8 = .3103326

There is a 31.03% probability that at least 6 were filed using the short form.

Is this correct?

Solution