Stuck on a probability question

[dbarron]

Hi, I am working through a worksheet of probability questions and I have got stuck on one question. I thought I knew how to calculate the answer but when I check my answer against the answer sheet my calculation is wrong and I cannot work out how to get the answer shown on the answer sheet, any help would be appreciated.

Two actuaries and four accountants are needed for the staff committee. The probability of an actuary being willing to join the committee is 0.3 and the probability of an accountant being willing to join the committee is 0.6. Calculate the probability that, out of a group of 10 actuaries and 10 accountants, there are exactly two actuaries and four accountants who are willing to join the committee.

I thought the answer is calculated as

0.3^2 * 0.6^4 * 6! / (2! * 3!)

But the answer given on the answer sheet is 0.026 and I'm afraid I cannot see past my solution.

 

[pka]

I think that this question is seriously miss-worded. At the very least it is misleadingly worded.
Please check the wording.

 

[Steven G]

I would assume that if someone was willing to join then the probability that they want to join would be 1 (ie 100% = certain).

So let's see what was probably meant by this problem. Goops, I really tried but I have no idea what was meant. Sorry

 

[Dr.Peterson]

Two actuaries and four accountants are needed for the staff committee. The probability of an actuary being willing to join the committee is 0.3 and the probability of an accountant being willing to join the committee is 0.6. Calculate the probability that, out of a group of 10 actuaries and 10 accountants, there are exactly two actuaries and four accountants who are willing to join the committee.

I thought the answer is calculated as

0.3^2 * 0.6^4 * 6! / (2! * 3!)

But the answer given on the answer sheet is 0.026 and I'm afraid I cannot see past my solution.

It makes perfectly good sense to me, and I get the same answer.

I chose to think of it this way:

Two red squares and four red triangles are needed. The probability of a square being red is 0.3 and the probability of a triangle being red is 0.6. Calculate the probability that, out of a group of 10 squares and 10 triangles, there are exactly two squares and four triangles that are red.​

Sounds rather binomial to me -- but doubly so!