The probability of event A is 0.6 and the probability of event B is 0.35. What could be the probability that only event B occurs?
I don’t understand why the answer here is anything other than 0.35? i’ve watched the video but still confused
To be clear, 0.35 should be correct.
Try drawing a Venn diagram.
I’m sorry this answer isn’t helpful. In the question am I to assume they’re independent but not mutually exclusive?
They need not be independent or mutually exclusive, but you can certainly use these cases as an example (if applicabnle).
Put it this way. If P(A and B) = P(B), what is the probability that only event B occurs? How does this look on a Venn diagram?
Again I’m sorry I’m not understanding?
Let’s put it this way.
Suppose you have two events A and B. The probability of event A occurring is 0.6, and 0.35 for B.
Can the probability of A and B occurring together be 0? Well, that’s when A and B are mutually exclusive. Is that possible?
Yes. Here’s why: a Venn diagram will be useful:
Notice that events A and B don’t intersect, which means that P(A and B) is 0.
Now we’ve determined that P(A and B) has to be at least 0. Can you deduce the upper bound of P(A and B)? Here’s a hint: when events A and B completely overlap in the Venn diagram (i.e, if B happens, A must also happen).
Let me know if you’re still facing trouble.