Question

If m and n are 2 numbers which belong to {1,2,3...100} then find Probability that 7^m + 7^n is divisible by 5.

Answer 1

there are 4 pairs (m,.n) which satisfies : (1,3),(3,1),(2,4),(4,2)
while all pairs 10P2

can you figure out the answer then ...

Answer 2

sorry missed a 0 :P

Answer 3

what, 100 ? bahhhh :)

Answer 4

sorry :|

Answer 5

see the result of exponents of 7 (just the units)
7^1 = 7
7^2 = ...9
7^3 = ...3
7^4 = ...1
7^5 = ...7
7^6 = ...9
7^7 = ...3
7^8 = ...1
......
......
and so on

as the total numberof outcames = 100P2

but still wonder how to get number of events, if i used trial too longggg
if m = 1, then n = {3,7,11,15,19,23,27,...,99}. there are 25 events
if m = 5, then n = {3,7,11,15,19,23,27,...,99}. there are 25 events too
..... --"

Answer 6

hmm..

Answer 7

continuing rad, im getting :-

2[25x25] + 2[25x25]
probability = ----------------------
100x100


= 1/4