practice_problems/problems/unit-01/probability-space/15

[giscus[bot]]

practice_problems/problems/unit-01/probability-space/15

https://mids-w203.github.io/practice_problems/problems/unit-01/probability-space/15.html

[awesome-eric]

Can the 2nd line of the solution for Minimum please be elaborated? I'm unable to intuit that logic jump...
For instance, if P(A) was .1 and P(B) was .2, then would the answer be -.5?

I'm confused. :(

[aquonAttheHub]

In the problem, notice that the chance of A or B happening (considering overlap) would be 1 since the chance of A happening summed with the chance of B happening exceeds 1. In an area diagram, this means that the region representing A cannot possibly fit in the sample space without overlapping with the region representing B.

When P(A) = 0.1 and P(B) = 0.2, there are no cases when the union of A and B take up the entire sample space. So P(AUB) cannot possibly be 1. The minimum value of P(A and B) would be when A and B are disjoint (P(AUB) = 0.1 + 0.2 = 0.3). In this case, P(A and B) = 0.2 + 0.1 - (0.3) = 0. I hope this helps!