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

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hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\((a^2+b^2)/10\) is integer

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968021756:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968165513:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968262315:dw

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3trying to understand...seeing this type of approach for first time...

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3how did u get a,b belongs t0 {......}mod 5 ?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968633462:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968728104:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968805888:dw

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3i think i am getting this a bit.....need to think

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351968902151:dw

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3can u expalin more on why there is just one option ?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2a and b are independent so P(a,b)=P(a).P(b)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3i think i got other parts, except that there is only 1 option

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351969216109:dw

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3ohh....right...i'll go through this again. thanks!

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1351969399186:dw

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3Also, any alternative approach will be appreciated....

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3@mukushla any other approach you can think of?

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1for some reason, i only have p = 0.10

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3me too, but thats incorrect.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1i found my error. it is as what mahmit gave. but i have a different proof.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1break 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.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1still polishing my argument.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0Use 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.

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1oops, i got 0.18 this time. hahaha. do you have the correct answer?

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1352033013459:dw

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3no, i don't have correct answer

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

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0Now what is probability:dw:1352033286386:dw

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0The 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?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3are both of you doing same thing ?

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3it will also contain 10 columns,right ? trying....

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1just 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

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3why is the answer drastically different from 2% ?

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.02 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

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1here'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)

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0Answer is \(\frac{14}{100}=0.14\).

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1i say it's 18/100, same as @Zarkon

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

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1the 2% only counted 5,5 and 0,0.

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0@sirm3d please write all the pairs.

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

Zarkon
 2 years ago
Best 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

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1here's the other nine (5,5) (6,2), (6,8) (7,1), (7,9) (8,4), (8,6) (9,3), (9,7)

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

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, my fault. Really  \(\frac{18}{100}\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3i got now, how we got 18 pairs for 100....

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1finally, we are all in agreement. hurrah.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3why consider only 100? will it make any difference, if we consider 1000 numbers ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3because if we consider only 10 numbers, we get different answer....

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.15^2 + 15^2 is divisible by 10, so is 5^2 + (10k+5)^2, so why bother bigger numbers, when the last digit suffices?

Zarkon
 2 years ago
Best ResponseYou've already chosen the best response.0you 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

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352043506996:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352043883988:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.20.18 is not true. 0.02 is true. Be sure.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3where's the fault in our discussion ?

sirm3d
 2 years ago
Best 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.

sirm3d
 2 years ago
Best 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?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352045197951:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352045432135:dw
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