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A point $P (x, y)$ is selected at random inside the square with boundaries $x = 0, y = 0$ and $x = 4, y = 4$ . The probability that P is inside the parabola $y^{2} = x$ is $\frac{k}{9}$ then $k$ is

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answer is 3.

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Detailed Solution

Total area = Area of the square $= 4 \times 4 = 16$

Favourable are = (Area above $x -$ axis under, parabola

$y^{2} = x$ from $x = 0 t o x = 4$ $= \int_{0}^{4} \sqrt{x} d x = \frac{16}{3}$

Req. Prob $= \frac{F a v . a r e a}{T o t a l a r e a} = \frac{1}{3}$

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