Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
hartnn
Group Title
If a,b are integers, what is the probability that \[a^2+b^2 \] is divisible by 10 ?
 2 years ago
 2 years ago
hartnn Group Title
If a,b are integers, what is the probability that \[a^2+b^2 \] is divisible by 10 ?
 2 years ago
 2 years ago

This Question is Closed

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

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

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

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

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
Is it clear?
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sirm3d Group TitleBest 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.
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
sorry,didn't get u...
 2 years ago

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

klimenkov Group TitleBest 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.
 2 years ago

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

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

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

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

sirm3d Group TitleBest ResponseYou've already chosen the best response.1
i got it, 0.18
 2 years ago

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

klimenkov Group TitleBest 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?
 2 years ago

sirm3d Group TitleBest ResponseYou've already chosen the best response.1
dw:1352033270108:dw
 2 years ago

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

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

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

sirm3d Group TitleBest 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
 2 years ago

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

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

Zarkon Group TitleBest 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
 2 years ago

sirm3d Group TitleBest 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)
 2 years ago

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

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

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

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

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

Zarkon Group TitleBest ResponseYou've already chosen the best response.0
I used Octave
 2 years ago

Zarkon Group TitleBest 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
 2 years ago

Zarkon Group TitleBest 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
 2 years ago

sirm3d Group TitleBest 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)
 2 years ago

hartnn Group TitleBest 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 ?
 2 years ago

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

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

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

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

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

sirm3d Group TitleBest 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?
 2 years ago

Zarkon Group TitleBest 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
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
aah! okk, got that....
 2 years ago

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

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

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
0.18 is not true. 0.02 is true. Be sure.
 2 years ago

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

sirm3d Group TitleBest 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.
 2 years ago

sirm3d Group TitleBest 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?
 2 years ago

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

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
dw:1352045432135:dw
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.