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If a,b are integers, what is the probability that \[a^2+b^2 \] is divisible by 10 ?
 one year ago
 one year ago
If a,b are integers, what is the probability that \[a^2+b^2 \] is divisible by 10 ?
 one year ago
 one year ago

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hartnnBest ResponseYou've already chosen the best response.3
\((a^2+b^2)/10\) is integer
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968021756:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968165513:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968262315:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
trying to understand...seeing this type of approach for first time...
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
how did u get a,b belongs t0 {......}mod 5 ?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968633462:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968728104:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968805888:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
i think i am getting this a bit.....need to think
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351968902151:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
can u expalin more on why there is just one option ?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
a and b are independent so P(a,b)=P(a).P(b)
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
i think i got other parts, except that there is only 1 option
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351969216109:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
ohh....right...i'll go through this again. thanks!
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1351969399186:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
Also, any alternative approach will be appreciated....
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
@mukushla any other approach you can think of?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
for some reason, i only have p = 0.10
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
me too, but thats incorrect.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
i found my error. it is as what mahmit gave. but i have a different proof.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
break the parity of a and b into oddodd, oddeven, evenodd and eveneven. clearly, p(oddeven) and p(evenodd) = 0 since the sum of squares is odd, not divisible by 2.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
still polishing my argument.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
Use this rule. If \(a\equiv x \mod 10 \) then \(a^2\equiv x^2 \mod 10 \) All different values for a can be 0,1,2,3,4,5,6,7,8,9,10. The probability that a is divisible by 10 is 1/10. Now find the values for \(a^2\) in mod 10.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
oops, i got 0.18 this time. hahaha. do you have the correct answer?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
dw:1352033013459:dw
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
no, i don't have correct answer
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
for a^2, probability is 1/6, i get that what about a^2+b^2
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
Now what is probability:dw:1352033286386:dw
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
The same table is for b. Now you have to write a table for \(a^2+b^2\) and watch what is for 0. Got it?
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
are both of you doing same thing ?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
Can you write a table for \(a^2+b^2\) ? With probabilities?
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
it will also contain 10 columns,right ? trying....
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
just count pairs that add up to 10 in my table. there should be 18 of them. (0,0), (1,3), (1,7), to list a few
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
If you want to get it, better to draw the whole table for \(a^2+b^2\).
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
why is the answer drastically different from 2% ?
 one year ago

ZarkonBest ResponseYou've already chosen the best response.0
2 5 0 7 6 7 0 5 2 1 5 8 3 0 9 0 3 8 5 4 0 3 8 5 4 5 8 3 0 9 7 0 5 2 1 2 5 0 7 6 6 9 4 1 0 1 4 9 6 5 7 0 5 2 1 2 5 0 7 6 0 3 8 5 4 5 8 3 0 9 5 8 3 0 9 0 3 8 5 4 2 5 0 7 6 7 0 5 2 1 1 4 9 6 5 6 9 4 1 0
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
here's the first half of (a,b) mod 10 (0,0), (1,3), (1,7), (2,4), (2,6), (3,1), (3,9), (4,2),(4,8)
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
Answer is \(\frac{14}{100}=0.14\).
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
i say it's 18/100, same as @Zarkon
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
why is the answer drastically different from 2% ? how is that table formed ? @Zarkon ?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
the 2% only counted 5,5 and 0,0.
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
@sirm3d please write all the pairs.
 one year ago

ZarkonBest ResponseYou've already chosen the best response.0
for i=1:10;for j=1:10;A(i,j)=mod(i^2+j^2,10);endfor;endfor
 one year ago

ZarkonBest ResponseYou've already chosen the best response.0
>> A A = 2 5 0 7 6 7 0 5 2 1 5 8 3 0 9 0 3 8 5 4 0 3 8 5 4 5 8 3 0 9 7 0 5 2 1 2 5 0 7 6 6 9 4 1 0 1 4 9 6 5 7 0 5 2 1 2 5 0 7 6 0 3 8 5 4 5 8 3 0 9 5 8 3 0 9 0 3 8 5 4 2 5 0 7 6 7 0 5 2 1 1 4 9 6 5 6 9 4 1 0 >> length(find(A==0)) ans = 18
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
here's the other nine (5,5) (6,2), (6,8) (7,1), (7,9) (8,4), (8,6) (9,3), (9,7)
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
also why are we only considering numbers till 100, will it make any difference, if we consider 1000 numbers ?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
Sorry, my fault. Really  \(\frac{18}{100}\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
i got now, how we got 18 pairs for 100....
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
finally, we are all in agreement. hurrah.
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
why consider only 100? will it make any difference, if we consider 1000 numbers ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
because if we consider only 10 numbers, we get different answer....
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
5^2 + 15^2 is divisible by 10, so is 5^2 + (10k+5)^2, so why bother bigger numbers, when the last digit suffices?
 one year ago

ZarkonBest ResponseYou've already chosen the best response.0
you are doing division by 10 (mod 10) there are only 10 numbers in that system. So we only need to consider the 10x10 possibilities to get the proportion
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1352043506996:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1352043883988:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
0.18 is not true. 0.02 is true. Be sure.
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
where's the fault in our discussion ?
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
@mahmit2012 what about the pairs 1,7 and 1,3? are they not solutions too? they were not counted in your argument.
 one year ago

sirm3dBest ResponseYou've already chosen the best response.1
@mahmit2012 you only saw 5,5 and 0,0 in your proof. that explains your 2/100=0.02. what about 1,7 pair?
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1352045197951:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.2
dw:1352045432135:dw
 one year ago
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