Bag of Balls

Puzzles
#1

Hi there,

Stats are really not my cup of tea. I have a problem with “4-Ultimate test” (and also test 5 but I would at least understand what is wrong with this one)
I tried to stick as much as possible to the concept of taking balls out of the bag.
I think I got a decent algorithm but I might be totally wrong.

Test 4-Ultimate test
inputs:
n=30 total nb of balls
w=10 nb of white balls
s=10 total nb of balls extracted
k=5 nb of white balls to be extracted

I get the following result

P(A)= 10 / 30 (white ball)
x 9 / 29 (white ball)
x 8 / 28 (white ball)
x 7 / 27 (white ball)
x 6 / 26 (white ball)
x 20 / 25 (black ball)
x 19 / 24 (black ball)
x 18 / 23 (black ball)
x 17 / 22 (black ball)
x 16 / 21 (black ball)
P(A)= 5168 / 10015005
P(!A)= 10009837 / 10015005
result: 5168:10009837
expected: 62016:414889

I don’t see what is wrong: is it my fraction simplification or the way I compute the stats ?
Any help will be greatly appreciated !

#2

It’s also possible to draw the black balls before the white (or in any other order like WBBBWB…), you only count one.

1 Like
#3

Ok I got it.
Thanks a lot eulerscheZahl !

#4

Hello this post makes me understood my error for the ultimate test 1

now i have 80 % and the ultimate test 2 that failed…
I can’t undestand my error since the result a nearly similary

60 balls
40 whites
50 balls taken
35 proba 35 whites… ?

i Do
2250829575120 * (C 50 35)
40/60* (white balls)
39/59*
38/58*
37/57*
36/56*
35/55*
34/54*
33/53*
32/52*
31/51*
30/50*
29/49*
28/48*
27/47*
26/46*
25/45*
24/44*
23/43*
22/42*
21/41*
20/40*
19/39*
18/38*
17/37*
16/36*
15/35*
14/34*
13/33*
12/32*
11/31*
10/30*
9/29*
8/28*
7/27*
6/26*
20/25* (blacks balls)
19/24*
18/23*
17/22*
16/21*
15/20*
14/19*
13/18*
12/17*
11/16*
10/15*
9/14*
8/13*
7/12*
6/11
my result
1235750079647531:7896812518143536 => 0.15648719996
expected result
134976:862537 => 0.15648719997

i can’t undestand why those result are so closed if i m wrong
any clue will be very lovely !
thx

#5

I use Window’s Calculator to do this division, got
0.15648719996939269532056443461388

So the last few digits are 9997 when simplified to the same number of digits as yours.

1 Like
#6

yes but i can’t undestand the ratio found (134976:862537) compared to mine, how the result could be so much factorized

#7

There could be a loss of precision in the middle of your calculation.
What language are you using?
What data type are you using to do the calculation?

2 Likes
#8

I use javascript,
I only do the multiply on the numerator and denominator;
Then i m looking for the largest common divider and divide all…
I m not sure to lose precision using multiply… but you may be right

#9

You could try using BigInt to verify the result. The correct fraction should be able to be reduced to two smaller integers.

2 Likes
#10

You are the winner, is use BigInt() for javascript and it works now…
Thx you @java_coffee_cup !

1 Like
#11

I have success on all test cases – so efficiency is now OK. I fail on validator 2.
As far as I can tell, I’ve dealt with all divide by zero cases so I don’t think I’m generating an error.
Would appreciate some guidance on where to look/what to improve.
Thanks!