1. ## Indepedence mutually exclusiveness

I'm working my way through my ACTEX study guide for the probability exam, and a question is really tripping me up. It goes like this:

You are given that p(a) = 0.5 and p(A union B) = 0.7.

Actuary 1 assumes A and B are independent and calculates p(B) based on that assumption.

Actuary 2 assumes A and B are mutually exclusive and calculates p(B) based on that assumption.

Calculating based on mutually exclusiveness isn't what's giving me problems, it's calculating when assuming independence.

If A and B are independent, and it says that the probability of A and B occuring equals 0.7, why isn't this problem solved by setting up an equation like this:

0.5 p(b) = 0.7 and solving for B? In my study guide, they solve it by using the compliments. Why is this only solved using the compliments? I don't understand the logic behind it. I know that it must be that way because if i solved it my way, the probability of B would be over 1. What am I missing here?

Furthermore, if i plugged in the probability of B, which is equal to 0.4 and multiply it by A, which is 0.5, it doesn't equal 0.7... I am so confused. XD

2. ## Re: Indepedence mutually exclusiveness

Originally Posted by seedofwinter
0.5 p(b) = 0.7 and solving for B?
That would be if you were told that P(A intersect B) = 0.7. Instead you know that P(A union B) = 0.7. Recall that P(A union B) = P(A) + P(B) - P(A intersect B)

3. ## The Following User Says Thank You to Dason For This Useful Post:

seedofwinter (01-06-2014)

4. ## Re: Indepedence mutually exclusiveness

I must be studying too hard. LOL I can't believe I made an error like that.

Thanks a lot, man.

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