Expert: Paul Klarreich - 4/8/2006

Question
Now let's assume that Sue and Ann do not study together, so whether one passes will be independent of whether the other passes. In other words, "Sue passes" and "Ann passes" are now assumed to be independent events, with probabilities 0.85 and 0.65 respectively.

   What is the probability both pass?

   What is the probability neither passes?

   If Ann passes, what then is the conditional probability that Sue passes?

Answer
Jason Asks in Category Calculus:
Subject:   
Question:  Now let's assume that Sue and Ann do not study together, so whether one passes will be independent of whether the other passes. In other words, "Sue passes" and "Ann passes" are now assumed to be independent events, with probabilities 0.85 and 0.65 respectively.

  What is the probability both pass?

  What is the probability neither passes?

  If Ann passes, what then is the conditional probability that Sue passes?
----------------------------------------------------------

You did say 'independent,' didn't you?  In that case:

p(A and S) = p(A) p(S) = 0.85 * 0.65
p(not A and not S) = p(not A) p(pot S) = 0.15 * 0.35

Conditional probability that Sue passes, given Ann passes.

You did say 'independent,' didn't you?  In that case:

p(S, given A) = p(S) = 0.85

That is, after all, what 'independent' means.  Knowledge about whether A occurred does not change the probability of S.