My google fu has failed me to find a method for this. I would assume there is a deterministed equation for what I'm trying to do but maybe it's more complicated than I am thinking.

I have two binary outcomes A and B, and I want to determine the probability of each scenario:

A=1, B=1

A=1, B=0

A=0, B=1

A=0, B=0

From my dataset, p(A)=0.56, p(B)=0.39 and correlation between them is -0.66. Is this enough information to determine the probability of the 4 possible scenarios? I'm a number of years out of any stats classes, so need a bit of help to get going in the right direction.

  • $\begingroup$ Yours is the case $p=0.56,$ $q=0.39,$ and $\rho=-0.66$ of the duplicate. You can just plug in the formulas or run the software solution given there. $\endgroup$
    – whuber
    Oct 8, 2021 at 16:31
  • 1
    $\begingroup$ Thanks, exactly what I needed! $\endgroup$
    – jsteinm1
    Oct 8, 2021 at 16:44


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