Simple task for anyone with the faintest idea about probability

Hi!

Yeah, I need help. Easy question for most math experts, I'd guess, but I just hate probability. So here goes...

Joe and his two friends were shooting balloons at a carnival. They all made one shot and hit two balloons. Their respective probabilites for hitting the balloons were as follows: 0.2 for both of Joe's friends and 0.6 for Joe himself. Find the probability that Joe was the one who missed the shot.

Yup, I get that you're apparently supposed to use the Bayes' formula, but that knowledge doesn't really help me. So any outside help would be appreciated!

Re: Simple task for anyone with the faintest idea about probability

Quote:

Originally Posted by

**JacobE** Joe and his two friends were shooting balloons at a carnival. They all made one shot and hit two balloons. Their respective probabilites for hitting the balloons were as follows: 0.2 for both of Joe's friends and 0.6 for Joe himself. Find the probability that Joe was the one who missed the shot.

Is it clear to you that the probability that exactly two hit a balloon is $\displaystyle (0.2)^2(0.4)+2(0.2)(0.8)(0.6)~?$

Can you explain why that is? What do you do with that?

Re: Simple task for anyone with the faintest idea about probability

Quote:

Originally Posted by

**Plato** Is it clear to you that the probability that exactly two hit a balloon is $\displaystyle (0.2)^2(0.4)+2(0.2)(0.8)(0.6)~?$

Can you explain why that is? What do you do with that?

Yeah, that much I figured out. The probability that exactly two balloons are hit forms up of either Joe missing ($\displaystyle (0.2)^2(0.4)$) OR either of his two friends missing ($\displaystyle 2(0.2)(0.8)(0.6)$).

But other than that, no, I don't know what to do with it.

Re: Simple task for anyone with the faintest idea about probability

Quote:

Originally Posted by

**JacobE** Yeah, that much I figured out. The probability that exactly two balloons are hit forms up of either Joe missing ($\displaystyle (0.2)^2(0.4)$) OR either of his two friends missing ($\displaystyle 2(0.2)(0.8)(0.6)$).

But other than that, no, I don't know what to do with it.

Let $\displaystyle T$ be the event that exactly two hit balloons.

You say that you see $\displaystyle \mathcal{P}(T).$

Suppose that $\displaystyle J$ is the event that Joe misses the balloon.

Now you want $\displaystyle \mathcal{P}(J|T)=~?$

Re: Simple task for anyone with the faintest idea about probability

I think that I finally got the idea of it.

Unless I made a misscalculation, the correct answer should be $\displaystyle \mathcal{P}(J|T)=0,04$.

If so, then thanks for the guidance!