Probability Distribution of 2 Defective Items (Help please)

[Moonlightbeam]

Hello this is my first time posting here. I am currently struggling on a Probability Distribution question about 2 Defective Items. The question is multiple choice but I don't really understand on how to tackle this problem. I don't really remember if theres some equation I am supposed to use.

A batch of 13 products is available for sampling. If only two products are defective, and you are randomly selecting 2 products, what is the probability that both products are defective?

• 1/13!
• 1/13
• 2/13
• 1/78

 

[HallsofIvy]

.There are 13 items and 2 are defective. The probability the first one you pick is defectivE is 2/13. If you did pick that one, that leaves 12 items, 1 of which is defective, so the probability the second one you pick is defective is 1/12. The probability both are defective is (2/13)(1/12)= (1/13)(1/6)= 1/78.

 

[LCKurtz]

Or, alternatively, there are [MATH]\binom {13}{2}[/MATH] ways to pick 2 from 13, one of which will work...

 

[Moonlightbeam]

Thank you so much

 

[Moonlightbeam]

.There are 13 items and 2 are defective. The probability the first one you pick is defectivE is 2/13. If you did pick that one, that leaves 12 items, 1 of which is defective, so the probability the second one you pick is defective is 1/12. The probability both are defective is (2/13)(1/12)= (1/13)(1/6)= 1/78.

So that means that the final answer should be 1/78 right?

 

[HallsofIvy]

That IS what I said!