Question

Medal and fan reward
Probability question

A bag contains 20 checkers 10 red and 10 black. Find the probability of selecting 2 black checkers when they are chosen at random WITHOUT replacement. Determine whether the event is dependent or independent.

answers:
dependent; 1/4
dependent; 9/38
independent; 1/4
independent; 9/38

Answer 1

Knowing that the experiment was done without replacement is important because it changes the probability of a black being drawn if you chose a black one on the 1st draw:

P(black on 1st Draw) = 10/20 = 1/2

But now, you need to find the probability of a black on the second draw. There are now only 9 black checkers in the bag and there are only 19 checkers total. So,

P(black on 2nd Draw) = 9/19.

Then, the probability of a black on the 1st draw AND the probability of a black on the 2nd draw is 10/20 * 9/19 = 90/380=9/38.

If you replaced the checker after the 1st draw, then the chance of black on the second would have been independent of the 1st. But that is not the case here -- the probability in the second draw is very much dependent on what was drawn before.

Note that the probability of black on the 2nd draw is about 0.47, which is significant compared to 0.5. With this small difference alone, you could win a lot of money in Las Vegas if you played the right game.

Answer 2

Ohhhh I was drawing two checkers at the same time like 8/18.
No wonder my answer was way off.

Answer 3

Thanks for your help.

Answer 4

NP