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Mathematics Question on Random Variables and its Probability Distributions

fx,y(x,y)={(x+y)0≤x≤1,0≤y≤1 0otherwise f_{x,y}(x,y)=\begin{cases} (x+y) & \quad 0\le x\le 1,0\le y\le 1 \\\ 0 & \quad \text{otherwise } \end{cases}
The Probability P(x+y≤1)P(x+y\le1) is:

A

23\frac{2}{3}

B

13\frac{1}{3}

C

16\frac{1}{6}

D

12\frac{1}{2}

Answer

13\frac{1}{3}

Explanation

Solution

The correct option is(B): 13\frac{1}{3}