Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Medium2 minQB

MathematicsMediuminteger

Two non-negative integers are chosen at random. The probability that the sum of their squares is divisible by 5 is $\frac{K}{25}$ then $k =$

Answer:

Solution:

Let the non-negative integers be $x, y, x = 5 a + α, y = 5 b + β$ where

$0 \leq α \leq 4, 0 \leq β \leq 4 x^{2} + y^{2} = 25 (a^{2} + b^{2}) + 10 (a α + b β) + α^{2} + β^{2} α^{2} + β^{2} is divisible by 5 α, β \in {(0, 0) (1, 2) (2, 1) (1, 3) (3, 1) (2, 4) (4, 2) (3, 4) (4, 3)} Probability = \frac{9}{25}, k = 9$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: QB

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