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Adding Independent Probabilities

What is the probability of my scoring either 1 or 2 on either one, or both, of my first two dice rolls?

P(1 or 2) on a given roll = 1/6 + 1/6 = 1/3
But now we can't just say that the answer is 2/3 because you can't add up mutually independent probs like that, only exclusive ones. So how do we get it?

Binomial - so X-B(2,1/3) and find P(X=1)? But that would find the probability of scoring 1 or 2 on 1 roll alone out of the 2 - where is the probability of scoring 1 or 2 on both?
Original post by Big-Daddy
Binomial - so X-B(2,1/3) and find P(X=1)? But that would find the probability of scoring 1 or 2 on 1 roll alone out of the 2 - where is the probability of scoring 1 or 2 on both?


You could use the binomial.

P(X>=1)= P(X=1)+P(X=2)
Reply 2
Original post by ghostwalker
You could use the binomial.

P(X>=1)= P(X=1)+P(X=2)


Ah I see. P(X≥1)=1-P(X≤0)=1-P(X=0)

So P(X≥1)=1-(2C0)*(1/3)0*(2/3)2-0=1-4/9=5/9. Correct?
(edited 10 years ago)
Original post by Big-Daddy
Ah I see. P(X≥1)=1-P(X≤0)=1-P(X=0)

So P(X≥1)=1-(2C0)*(1/3)0*(2/3)2-0=1-4/9=5/9. Correct?


Yep!

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