In a shipment of 21 parts, four of the parts are defective. If three parts are selected at random without replacement, find the probability that :

a.) All three parts selected are defective.

4/21*3/20*2/19=.003

b.) None of the tree parts selected are defective.

3/17*2/16*1/15=.001

c.) At least one of the tree parts selected is defective.

4/21*20/20*19/19=.190

Question~ Are all these answers correct?
If not, what am I doing wrong?

I'm also questioning c.) I'm not sure I did that one correctly. Can someone go over this problem with me? I would so greatly appreciate it.

Thank you!

If they say at least one, it is easier to do the question by finding NONE and subtracting that number from 1. At least one would mean, 1, 2 or 3.

I agree with a and b.

for c, take 1- .001 = .999

Let's go through each part of the problem and check the results:

a.) All three parts selected are defective.
To calculate the probability of this event, you correctly used the formula for dependent events without replacement. The probability of selecting the first defective part is 4/21, the second defective part is 3/20 (since there is one less defective part and one less total part), and the third defective part is 2/19. Multiplying these probabilities together gives 0.003, which is the correct answer.

b.) None of the three parts selected are defective.
Here, it seems you made a mistake. To find the probability of selecting three non-defective parts, we need to consider the number of non-defective parts in the shipment, which is 21 - 4 = 17. So the probability of selecting the first non-defective part is 17/21, the second non-defective part is 16/20, and the third non-defective part is 15/19. Multiplying these probabilities together gives 0.049, not 0.001 as you calculated. So the correct answer is 0.049.

c.) At least one of the three parts selected is defective.
To find the probability of at least one defective part, we can calculate the complement probability and subtract it from 1. The complement probability is the probability of selecting no defective parts. You already calculated this in part b (0.049). So the probability of at least one defective part is 1 - 0.049 = 0.951, not 0.190 as you calculated.

So to summarize the correct answers are:
a.) 0.003
b.) 0.049
c.) 0.951

I hope this clarifies the problem for you. If you have any further questions, feel free to ask!