SOLUTION: I was just wondering if someone could double check my work on this problem: A box contains 8 good parts and 4 defective parts. If a sample of 2 parts is drawn from the box at rand

Algebra ->  Probability-and-statistics -> SOLUTION: I was just wondering if someone could double check my work on this problem: A box contains 8 good parts and 4 defective parts. If a sample of 2 parts is drawn from the box at rand      Log On


   

Question 359390: I was just wondering if someone could double check my work on this problem:
A box contains 8 good parts and 4 defective parts. If a sample of 2 parts is drawn from the box at random (without replacement), what is the probability of each of the following:
Two good parts are selected. (my answer 8/12 * 7/11 = 14/33 or 42%)
Two defective parts are selected. (my answer 4/12 * 3/11= 1/11 or 9%)
One good part is selected first, and then one defective part is selected second?
(my answer 8/12 or 66% chance of good part first, 4/11 or 36% chance of defective part being chosen second 8/12 * 4/11 = 8/33 or 24% totalling a 24% chance)
Exactly one defective part out of the two is selected. (my answer ?)
Any input would be apprieciated!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.Two good parts are selected.
P%28G%2CG%29=14%2F33 , Correct!
.
.
2.Two defective parts are selected.
P%28D%2CD%29=1%2F11, Correct!
.
.
3.1st good, 2nd defective.
P%28G%2CD%29=8%2F33, Correct!
.
.
Exactly one defective part out of the two is selected.
.
.
You already have half of the answer (P%28G%2CD%29=8%2F33).
What about if you choose a defective part first, then a good part.
That would give you P%28D%2CG%29
P(exactly 1)=P%28D%2CG%29%2BP%28G%2CD%29
P(exactly 1)=P%28D%2CG%29%2B8%2F33
.
.
Also,remember there are only 4 choices you can make, picking two parts.
GG-P%28G%2CG%29=14%2F33
DD-P%28D%2CD%29=1%2F11
GD-P%28G%2CD%29=8%2F33
DG-P%28D%2CG%29=??
Remember also that the sum of the probability for all of the events must be 1.
So you can solve this problem in two ways, or use the other way to check your work.