The probability that the sum of squares of two non-negative integers i

1.	The probability that the sum of squares of two non-negative integers is divisible by 5 is(a) 7/25(b) 8/25(c) 9/25(d) 2/25
Answer» Correct option (c) 9/25 Explanation: Let two non-negative integers be x & y such that x = 5a + α and y = 5b + β where 0 ≤ α, ≤ β New, x²+ y² = 25(a²+ b² ) + 10(aα + bβ)+ α² + β² α² + β²should be divisible by 5 (α ,β) can have ordered pairs as {(0,0), (1,2), (2,1), (1,3), (3,1), (2,4), (4,2), (3,4), (4,3)} = 9 ways required probability is 9/25

The probability that the sum of squares of two non-negative integers is divisible by 5 is(a) 7/25(b) 8/25(c) 9/25(d) 2/25

Answer»

Correct option (c) 9/25

Explanation:

Let two non-negative integers be x & y such that x = 5a + α and y = 5b + β where 0 ≤ α, ≤ β

New, x²+ y² = 25(a²+ b² ) + 10(aα + bβ)+ α² + β²

α² + β²should be divisible by 5

(α ,β) can have ordered pairs as

{(0,0), (1,2), (2,1), (1,3), (3,1), (2,4), (4,2), (3,4), (4,3)} = 9 ways

required probability is 9/25

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The probability that the sum of squares of two non-negative integers is divisible by 5 is(a) 7/25(b) 8/25(c) 9/25(d) 2/25

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