Roland2rule wrote:If two different numbers are to be selected from set {1, 2, 3, 4, 5, 6}, what is the probability that the sum of two numbers is a square of an integer?
A. 1/2
B. 1/3
C. 1/5
D. 1/9
E. 1/30
can anyone assist me with this question? Thanks
Probability that the sum of two numbers is a square of an integer is given by "(Number of pairs that make the sum a perfect square) / (Total number of selections of two numbers out of the given six numbers)"
Total number of selections of two numbers out of given six numbers = 6C2 = (6.5) / (1.2) = 15;
To get the value of 'Number of pairs that make the sum a perfect square,' you should use the brute force. Add all the possible pairs of two numbers from the set and see which of the pairs render 4 (min. possible value) or 9 (max. possible value).
We see that only three pairs qualify: {1, 3); {3, 6}; and {4, 5}
Thus, the probability that the sum of two numbers is a square of an integer = [spoiler]3/15 = 1/5[/spoiler].
The correct answer:
C
Hope this helps!
-Jay
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