Determining probability involving normal random variables and given covariance

Say X and Y are normally distributed random variables, i.e., X,Y ~ N(0,1). For some fixed t and c I know that Pr[X≥t]=c and Pr[Y≥t]=c. Moreover, I also know that X and Y have covariance 0.999.

How can I deduce what Pr[X≥t and Y≥t] roughly is?

Bonus question: what are good references to learn more on related topics for normally distributed random variables?

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