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
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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) (Show Source): You can put this solution on YOUR website!
Let , then we observe that ,, and ends in ,, and respectively.
Thus, ends in ,, and according as it is of the form , , and respectively.
If is the sample space, then
is divisible by , if:
(1) is of the form and is of the form or
(2) is of the form and is of the form or
(3) is of the form and is of the form or
(4) is of the form and is of the form
So, number of favorable ordered pairs (,)=
Required probability =
​answer:
.
a.
Answer by ikleyn(52778) (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/
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