What are the odds that you would pick the right 2 out of 20?

Question

There a contest going that will require you to pick 2 bags (with winning certificates) out of 20. The other 18 bags are losers.

Please give me the odds in a percentage so it's easier for me to understand.

Answer 1

The probability of choosing the first correct bag would be 2 in 20. (As there are 2 good bags in 20).
= 2 / 20
= 1 / 10
= 0.10
= 10 %

Now 19 bags remain, and presuming that you did choose the good bag the first time, there is only 1 good bag in them.
So the probability of choosing the good bag is 1 in 19.
= 1 / 19
= 0.05263
= 5.263 %

Now to find the probability of getting the good bag the first AND the second time, you just have to multiply the probabilities of the two situations.
= 0.10 * 0.05263
= 0.005263
= 0.5263 %
= very poor odds.

(I did not mutiply the probability percentages (10 % and 5.263%) as this product will NOT be the product of probablities BUT the product of probability percentages.
That is [0.10 * 100] * [0.005263 * 100]
That is 0.10 * 0.005263 * 100 *100!!
That would be wrong, wouldn't it?)

Answer 2

If you are required to pick two bags at the same time there is only one combination that is the winner. The combination of 20 things taken 2 at a time is 190. So you see that both ways the the percentage is 1/190 which gives odds of 1 to 189

Answer 3

th probability of picking one of the bags the first time is 2/20, or 1/10. after picking one correctly, the probability of picking the other is 1/19, because only one bag remains out of 19 total remaining. to find the total probability, multiply the two together:

(1/10)*(1/19) = 1/190

however, odds are different than probability... although the two ideas are directly related. you can express probability as a percentage (in this case just over one half of one percent), or by reading the fraction aloud, "the probability is one in one hundred ninety." the odds, though, have to be expressed as a ratio, and this ratio must ADD UP TO the denominator of the reduced probability fraction, like this:

189:1 ("one hundred eighty-nine to one")

this represents the same thing as the probability.

Answer 4

I think it should be 2/20 = 1/10

Answer 5

Total no. of ways of picking up any 2 bags out of 20 is
n = 20C2 = 190

No. of ways of picking up 2 right bags out of 2 is
r = 1.

Hence, by classical definition of probability,
probability of picking up right bags is
1 / 190
=100/190 %
= 0.5263 %

Answer 6

1 out of 20 choose 2.

Answer 7

probability = 1/(20C2) = W/(W+L) = odds/(odds+1)
(20C2)odds = odds+1
odds = 1/(20C2-1) = 1/189 = 0.53%