Answer:
The probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
Explanation:
It is provided that the random variables X and Y follows a standard normal distribution.
That is,

It is also provided that the variables X and Y are statistically independent of each other.
Compute the probability that X and Y are both positive and that their sum is less or equal to 1 as follows:
The mean and standard deviation of X + Y are:

The probability is:
![P(X+Y\leq 1)=P(X+Y<1-0.50)\ [\text{Apply continuity correction}]\\](https://img.qammunity.org/2021/formulas/mathematics/college/xtcm0g7mgyoo3r2b7m0w9v887snoqnfpzc.png)

*Use the z-table.
Thus, the probability that X and Y are both positive and that their sum is less or equal to 1 0.64.