4 - Pi is the area outside circle, you need to divide by total area that is 4 also.

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Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1, 1]$. The probability that $X^{2}+Y^{2}>1$ is

- $\pi/4$
- $1-\pi/4$
- $\pi/2 - 1$
- Probability that $X^{2}+Y^{2}<0.5$
- None of the above.

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Best answer

Area of square denotes the total probability, i. e, 1.

Area of circle denotes P(X ^{2 }+ Y ^{2 }≤ 1)

Area of shaded region denotes the required probability, i.e, P(X ^{2}+ Y ^{2} >1)

Area of shaded region=Area of square -Area of Circle

= 4 - ⊼

= 4 ( 1 - ⊼/4)

If area of square corresponds to total probability, then

4 sq.unit=1

= 1 sq.unit=1/4

= 4(1-⊼/4) sq.unit=

=1- ⊼/4

which is the required probability.

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