An IRS auditor randomly selects 3 tax returns from 58 returns of which 8 contain errors. What is the probability that she selects none of those containing errors?

number of all possible selections = C(58,3) = 30856

number of error-less selections = C(50,3) = 19600

prob to select non-error = 19600/30856 = 4900/7714
= 350/551

(50/58)*(49/57)*(48/56) = 0.635

63.5%

Go with drwls method, his is more direct.

Well, when it comes to taxes and IRS auditors, it's always a good thing to avoid errors. So let's crunch some numbers and calculate the probability.

There are 58 tax returns in total, and 8 of them contain errors. The auditor randomly selects 3 tax returns. We want to find the probability that none of those 3 selected tax returns contain errors.

To calculate this, we need to determine the number of "good" tax returns (ones without errors) and divide it by the total number of possible combinations of 3 tax returns.

The number of good tax returns is 58 (total) - 8 (with errors) = 50.

The total number of combinations of selecting 3 tax returns from 58 is given by the binomial coefficient "58 choose 3."

So, the probability of selecting none of the tax returns containing errors is:

(50 choose 3) / (58 choose 3).

But hey, why get into all the complicated math when I can just tell you the answer? The probability is approximately 0.824 or 82.4%.

Remember, humor is a great way to distract yourself from the stress of taxes!

To find the probability that the auditor selects none of the returns containing errors, we need to find the probability of selecting a correct return each time.

First, let's find the total number of correct returns. Out of the 58 returns, 8 contain errors. So, there are 58 - 8 = 50 returns without errors.

To calculate the probability of selecting a non-error return on the first selection, we divide the number of correct returns by the total number of returns: P(selecting a non-error return on the first selection) = 50/58.

After selecting a non-error return on the first selection, there will be 57 returns left, with 49 non-error returns remaining.

To calculate the probability of selecting a non-error return on the second selection, we divide the number of non-error returns by the total number of remaining returns: P(selecting a non-error return on the second selection) = 49/57.

Finally, after selecting a non-error return on the second selection, there will be 56 returns left, with 48 non-error returns remaining.

To calculate the probability of selecting a non-error return on the third selection, we divide the number of non-error returns by the total number of remaining returns: P(selecting a non-error return on the third selection) = 48/56.

Now, to find the probability of selecting none of the returns containing errors, we multiply the probabilities of selecting a non-error return on each selection:

P(selecting none of the returns containing errors) = P(selecting a non-error return on the first selection) * P(selecting a non-error return on the second selection) * P(selecting a non-error return on the third selection)
= (50/58) * (49/57) * (48/56)

Thus, the probability that the IRS auditor selects none of the returns containing errors is approximately 0.462 (or 46.2%).

find the probability of tossing 5 tails, then 5heads, on the 10 tosses of a fair coin