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I have a database that gives me how common the next chord in a chord progression is.

For example, 20% of chord progressions start with I chord. Of those progressions, 36% have V next, then 38% have vi next, then 75% have IV next.

From that, can I calculate how common the I-V-vi-IV chord progression is out of all 4 chord progressions? Can I just multiply out the probabilities i.e. .2 * .36 * .38 * .75? So I-V-vi-IV is about 2% of all chord progressions? Is that correct?

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    I believe that's correct. – 2017-01-09
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    Assuming your percentages are conditional probabilities given all of what has gone before: $75\%$ of progressions starting I-V-vi are immediately followed by IV, rather than $75\%$ of vi chords being followed by IV – 2017-01-09
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    Yes, conditional probabilities given all of what has gone before – 2017-01-09

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