What's the formula for this problem?

Question

P (G) = 0.5

P (H) = 0.3

P( H | G) = 0.6

Find P (H OR G)

What's the formula for (H OR G)? I just don't know where to plug in the numbers/how to set it up. Thanks for your help.

Answer 1

If P(G) = .5 and P(H|G) = .6, as P(H|G) = P(HG)/P(G), P(HG) = P(G)P(H|G) = .5 * .6 = .3

As P(H) = .3, P(HG')) = P(H) - P(HG) = .3 - .3 = 0

P(G') = 1 -P(G) = .5

Then, P(G'H') = P(G') - P(G'H) = .5 - 0 = .5

Then, P(H ∪ G) = 1 - P(G'H') = 1 - .5 = .5