Question

Statistics anyone?
NOTE: this is a made up question lol. I just wanna practice.

Suppose you just received a shipment of 14 televisions. Two of the televisions are defective. If two televisions are randomly​ selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not​ work?

Answer 1

12 TVs work, so the probability of the first tv working is 12/14.

The probability of the second working is then 11/13. Assuming you select the TVs without replacement.

Multiply those.

Answer 2

For the probability at least one works, you have three possible situations:

First tv works, second doesn't. First doesn't work, second does. Or both don't work.

Find the probability for each of those three, then add them together.

Answer 3

Another way to find the probability that both of the televisions in the sample work is to use combinations:
\[\large P(both\ work)=\frac{12C2}{14C2}\]

Answer 4

I have to give you credit. I've never seen that before.

Answer 5

Never seen combinations used for probability before? It's equivalent to doing what I did, just using combinations formula.

Answer 6

No, I had different crazy formulas. Just that specific way, no I haven't.

Answer 7

0.275 would be the answer correct?

Answer 8

The method that I used (combinations) is used for sampling without replacement.

Answer 9

Gotcha! Thanks!!

Answer 10

0.275 or 0.725?

Answer 11

0.275

Answer 12

It should be 0.725. How'd you get such a low result?

Answer 13

I'm not sure, my calculator told me lol

Answer 14

lol well what did you tell your calculator to do?

Answer 15

Idk some stuff

Answer 16

Such as...