Help with proving probability equations

**jennyk** · October 11th 2012, 01:06 PM

Hey, if anyone has time to give me some guidance on how to prove these i would be so grateful

thank you... :

i) P(A∩B) ≥ P(A) +P(B)−1,
ii) P(A∆B) = P(A) +P(B)−2P(A∩B)

**Plato** · October 11th 2012, 01:28 PM

Originally Posted by jennyk

i) P(A∩B) ≥ P(A) +P(B)−1,
ii) P(A∆B) = P(A) +P(B)−2P(A∩B)

$1\ge\mathcal{P}(A\cup B)=\mathcal{P}(A)+\mathcal{P}(B)-\mathcal{P}(A\cap B)$

**jennyk** · October 11th 2012, 02:05 PM

Thanks but i don't follow/understand this. Maybe i'm hopeless but something more step by step would be great

**Plato** · October 11th 2012, 02:16 PM

Originally Posted by jennyk

Thanks but i don't follow/understand this. Maybe i'm hopeless but something more step by step would be great

You can't solve $1\ge a +b-c$ for $c\ge ~?$
If you cannot then you need help at a far deeper level than you can get anywhere online.

Thread: Help with proving probability equations