the pearls

Hi usamashaker. I can get the odds down to 74.9%. However, Mark is the wizard with this type of question, if nobody can come up with anything better I will post my full answer.

In the meantime:

What if you have three vases: one vase containing two white pearls, one vase containing one white and one black pearl, and one vase containing two black pearls. From one of these vases, a pearl is taken. This pearl turns out to be white. What is the probability that the other pearl in the same vase is also white?

usamashaker: 298/398
Tryagain: 2/3

100 white in one flask
100 black in the other
chance's 50-50

I think if you put 100 white pearls in, covered them with 99 black pearls in one flask and in the other flask you put one black pearl you would increase your odds.

Hi try

try say
74.9%
mark say
298/398

usams say
that's correct
put your full answer buddy

carditel
it can be higher


boomerang
it would be 74.9%
you will choose randomly from the top or the botom

The probability of a black pearl from the first vase is 1, and the probability of a black pearl from the second vase is 99/199. The total probability of a black pearl is 0.5 × 1 + 0.5 × 99/199 = 298/398 (approximately 74.9%).



Mark:

Three jars 2/3


There are three pearls that can be the white pearl that was taken from the chosen vase:
The first pearl from the vase with two white pearls: in this case, the other pearl is also white. The second pearl from the vase with two white pearls: in this case, the other pearl is also white. The white pearl from the vase with one white and one black pearl: in this case, the other pearl is black.
The probability that the other pearl in the same vase is also white, is therefore 2/3.




Ok, now you have ten vases. Five of the vases contain a white pearl and four of the vases contain a black pearl (note that a vase may contain both a white and a black pearl!). You randomly select one of the ten vases.

What is the probability that the vase you chose is empty

[C(5,4)*C(5,0)*5/10 +
C(5,3)*C(5,1)*4/10 +
C(5,2)*C(5,2)*3/10 +
C(5,1)*C(5,3)*2/10 +
C(5,0)*C(5,4*1/10] / C(10,4)
= 3/10

Mark:

[C(5,4)*C(5,0)*5/10 +
C(5,3)*C(5,1)*4/10 +
C(5,2)*C(5,2)*3/10 +
C(5,1)*C(5,3)*2/10 +
C(5,0)*C(5,4*1/10] / C(10,4)
= 3/10


The probability that the chosen vase does not contain a white pearl is (10-5)/10 = 1/2. The probability that the chosen vase does not contain a black pearl is (10-4)/10 = 3/5. The probability that the chosen vase does not contain any pearl is therefore 1/2 × 3/5 = 3/10 (which is 30%).

I guess I did it the hard way.

Cheer up dude, think of the other 9999 times you did it in an easier way than I.