# Joint Probability Given

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


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).