Thread: Prove the probability statement

Let events A, B and C be independent. Show that (A union B) and C are independent.

Attempt at solution:

Setup: If [A intersection B intersection C] = [A][B][C], then show that [(A union B) intersection C] = [A union B][C].

I'm not sure how to go about doing this. Would using conditional probability theorem be a good start?

Originally Posted by My Little Pony

Let events A, B and C be independent. Show that (A union B) and C are independent.

Attempt at solution:

Setup: If [A intersection B intersection C] = [A][b][C], then show that [(A union B) intersection C] = [A union B][C].

I'm not sure how to go about doing this. Would using conditional probability theorem be a good start?

Suppose events , and are independent. Then,

, , and

.

Now, , by the distributive law.

So,







, as was to be shown.

All that was needed to prove this was the distributive law, multiplicative law of probability, and the additive law of probability.