# What is the probability of this home work question?

In a lot of 12 washing machines, there are 3 defective pieces. A person has ordered 4 washing machines. Find the probability that all the four are good.

probability of a machine being undefected = 9/12 (3/4)

so probability of four machine being good should be =(3/4)^4

How is that incorrect? Can anyone please point me out?

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When you take the first machine, and it is good, you do not have anymore 12 machines to choose, but only 11! And of these, only 8 are good. Try to proceed from here. – guaraqe Apr 17 '13 at 22:22
Calculate the probability of a machine being good, then remve a good machine, calculate the probability of a machine being good, remove the machine, what is the answer for 4 machines being good? – Arjang Apr 17 '13 at 22:23
Your answer is correct if you choose a machine, see if it is good, put it back into the pool, choose again (so maybe the same one, maybe not), etc. It is also close to correct if you have a large pool that is $75\%$ good, so removing one doesn't change the composition of the pool very much. – Ross Millikan Apr 17 '13 at 22:29

The first one has probability $9/12$ of being good (9 good ones and 12 in total). Now we take this good one. The second one has probability $8/11$ of being good. The third one has probability $7/10$ of being good. The last one has probability $6/9$ of being good. This gives us:
$$\frac9{12} \cdot \frac8{11} \cdot \frac7{10}\cdot \frac69 = \frac{14}{55}$$