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 .
My working :
X-B(4 , 0.75)
P(X=4) = 4C4(0.75)^4 (0.25)^0 = 81/256
But my answer is wrong . Where is my mistake again ? Thanks
It's better to think like this: there are, to start with, 12 machines, 9 of which are good. The probability that the first machine selected is good is 9/12= 3/4. Assuming that happens, there are now 11 machines, 8 of which are good. The probability that the second machine selected is good is 8/11. Assuming that happens, there are now 10 machines, 7 of which are good. The probability the third machine is selected is 7/10. Finally, we have 9 machines left, 6 of which are good and the probability that the fourth machine selected is good is 6/9= 2/3. We can assume each selected was good because we are only calculating the probability that all four selected are good: it is (9/12)(8/11)(7/10)(6/9)= (3/4)(8/11)(7/10)(2/3)