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I've seen this question floating around:

The joint probability of events A and B is 32 percent with the probability of event A being 60 percent and the probability of event B being 50 percent. Based on this information, the conditional probability of event A given event B has occurred is closest to:

The answer is 32%/50% = 64%.

My question, where does the stated 32% joint probability come from?

If joint prob of A and B is P(AB), shouldn't the problem say?

The joint probability of events A and B is `30 percent`
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If events A and B were known to be independent of each other, you could calculate the joint probability with $.6 \times .5 = .3$. But since the problem doesn't assume that they're independent, then the joint probability could be anywhere from 10% (smallest possible overlap) to 50% (event B always occurs with event A).

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  • $\begingroup$ Just to be sure, the overlap is simple math: Minimum (.6 - .5) and Maximum(.6, .5)? $\endgroup$
    – miler350
    Commented Nov 12, 2015 at 13:33
  • $\begingroup$ Minimum = (.6 - .5) * and Maximum = Minimum(.6,.5)* $\endgroup$
    – miler350
    Commented Nov 12, 2015 at 14:15
  • $\begingroup$ To get the minimum, .6 + .5 - 1, because the total probability can't be greater than 1 in real life, so if .6 + .5 adds up to something >1, we know that extra 0.1 has to be due to overlap. You're exactly right about the maximum. $\endgroup$
    – wmay
    Commented Nov 12, 2015 at 14:24

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