Math Help - [SOLVED] Simple probability question

1. [SOLVED] Simple probability question

2 events that are independent of each other.
p(a) = .5 and p(b) = .95
What is the probability that b or a, or both b and a?

I know b and a is p(a)*p(b) but my book doesn't seem to cover both.

Thanks!

2. Probability

Hello othnin
Originally Posted by othnin
2 events that are independent of each other.
p(a) = .5 and p(b) = .95
What is the probability that b or a, or both b and a?

I know b and a is p(a)*p(b) but my book doesn't seem to cover both.

Thanks!
I think a probability tree is the easiest way to understand this. See the attached diagram.

The four end-points describe, with their respective probabilities, the possible outcomes. If you want to know the probability of arriving at more than one of these, just add their probabilities together.

So, for instance, the probability of one of a or b but not both is 0.5 x 0.05 + 0.5 x 0.95 = 0.5; and the probability of a or b or both is 0.5 x 0.95 + 0.5 x 0.05 + 0.5 x 0.95 = 0.975.

Does that make it clearer?