SOLUTION: If the integers m and n are chosen at random from 1 to 100, then what is the probability that a number of the form 7^n+7^m is divisible by 5 a. 1/4 b. 1/2 c. 1/8 d. 1/3

Algebra ->  Probability-and-statistics -> SOLUTION: If the integers m and n are chosen at random from 1 to 100, then what is the probability that a number of the form 7^n+7^m is divisible by 5 a. 1/4 b. 1/2 c. 1/8 d. 1/3      Log On


   

Question 1204254: If the integers m and n are chosen at random from 1 to 100, then what is the probability that a number of the form 7^n+7^m is divisible by 5


a. 1/4 b. 1/2 c. 1/8 d. 1/3
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


Let I=7%5En%2B7%5Em, then we observe that 7%5E1,7%5E2,7%5E3 and 7%5E4 ends in 7,9,3 and 1 respectively.

Thus, 7%5E1 ends in 7,9,3 and 1 according as it is of the form 4k+%2B+1, 4k+%2B+2, 4k+-+1 and 4k+respectively.

If S is the sample space, then n%28S%29=%28100%29%5E2

7%5Em%2B7%5En is divisible by 5, if:

(1) m is of the form 4k+%2B+1 and n is of the form 4k+-+1 or
(2) m+is of the form+4k+%2B+2 and n is of the form 4k or
(3) m+is of the form 4k+-+1 and n is of the form+4k+%2B+1 or
(4) m is of the form 4k and n is of the form 4k+%2B++2

So, number of favorable ordered pairs (m,n)=4%2A25%2A25
Required probability = %284%2A25%2A25%29%2F%28100%29%5E2=+1%2F4
​answer:
.
a. 1%2F4+


Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!


The content of the @MathLover1 post is copy-pasted without reference from this web-page

https://www.toppr.com/ask/en-us/question/if-the-integers-m-and-n-are-chosen-at-random/