SOLUTION: Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 4 yellow disks numbered 7 through 10, find the probabilit

Question 1080909: Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 4 yellow disks numbered 7 through 10, find the probability of selecting a yellow disk, given that the number selected is less than or equal to 3 or greater than or equal to 8.
From the other answers on this website, I can see that:
6 Red, 4 Yellow. 3 are numbered 1,2,3 (less than or equal to 3) and are red; 3 are numbered 8, 9, 10 (greater than or equal to 8) and are yellow. The disk selected is one of those 6. Three are red, three are yellow. Therefore, there are 3 chances out of 6 that the disk will be yellow, which reduces to 1/2 or 0.50.
MY QUESTION: Why don't you multiply the chances of getting a yellow (4 out of 10) by the chances of getting correct number (6 out of 10), which would be 6/25?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The short answer is that the numbers given determine the disk, not the fact that two disks are being chosen. There are 6 possible numbers chosen, and half of them will produce a yellow.
The longer answer is that these are not independent events, which would allow one to multiply the probability. The number and the disk are not independent; one determines the other. There is a probability of getting a yellow of 4/10 with the first choice, and then it is 3/9. But the choices are CONDITIONAL upon a certain number's being allowed.
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