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The very first test case is wrong. Puzzle description clearly explains that the answer is “1:3” while the answer inside the example AND the test case is “1:2”.
So the ratio P(A) : P(!A) is 1:2 (read 1 to 2).
I see an explanation, why the answer is 1:2 there.
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 !
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
Ok I got it.
Thanks a lot eulerscheZahl !
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
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
yes but i can’t undestand the ratio found (134976:862537) compared to mine, how the result could be so much factorized
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
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
You could try using BigInt to verify the result. The correct fraction should be able to be reduced to two smaller integers.
2 Likes
You are the winner, is use BigInt() for javascript and it works now…
Thx you @java_coffee_cup !
1 Like
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!
Hmmm, can someone give me some help? ^^
I constantly fail the 5th test (and validator), answer found being: 16389258350763:104732261513840.
I’m using Python, and only ints for this, so no rounding error, no overflow (int has no max value), etc…
The way I solved it is computing the probability in two separate ints: the numerator and the denominator (to avoid rounding errors), (let’s call them a and d, so P(A)=a/d and P(!A)= b/d, b=d-a) and print a:b after having divided them both by gcd(a,b)
I know that mathematically, my answer is correct, so I’m wondering what programming error could potentially cause this to happen
(Note that I pass every other test and validator
Could you show the steps you took, using the inputs 60, 40, 50, and 35, that led to the two numbers?
… Wth, I just ran it again, changing a little bit of syntax for clarifying the code (really didn’t change any actual calculation, just things like int(a/b) to a//b where it was anyway giving an int), and now it works???
But with 60 40 50 35, it was computing:
a= binomial(35,50) * 40!/(40-35)! * (60-40)!/(60-40-(50-35))!
b= 60!/(60-50)! - a
g=gcd(a,b)
print a//g : b//g
(the d I was talking about being the 60!/(60-50)! that I don’t actually need to compute since it’s cancelled when comparing P(A):P(!A))
Now it’s the same thing, but with //'s instead of /'s, and it’s suddenly working…