probability question (1 Viewer)

[sadpwner]

There are 3 separate targets. 1 cannot be destroyed and can be shot at infinitely. The other 2 can be destroyed if shot at once by an arrow. 5 arrows are fired randomly one by one. What are the odds that both destroy-able targets are destroyed? The destroyed targets cannot be shot at again. All arrows hit.

My attempt at the first question.
The odds of it hitting the undestroyable target 4 times
2/3 x (1/2)^4 + 1/3 x 2/3 x (1/2)^3 + 1/3 x 1/3 x 2/3 x (1/2)^2 + (1/3)^3 x 2/3 x 1/2 + (1/3)^4 x 2/3

The odds of hitting the undestroyable target 3 times
2/3 x 1/2 + 1/3 x 2/3 x 1/2 + (1/3)^2 x 2/3 x 1/2 + (1/3)^3 x 2/3 x 1/2

Then add them both up up giving the answer. I am pretty sure you have to do separate cases.

That gives 0.6023662551440329
There are 3 separate targets. 1 can be destroyed if shot at 4 times but will end the game in doing so. The other 2 can be destroyed if shot at once by an arrow. 5 arrows are fired randomly one by one. What are the odds that both destroy-able targets that are destroyed by one shot are destroyed? The destroyed targets cannot be shot at again. If the game is over, no more arrows can be shot. All arrows hit.

 

[Drsoccerball]

There are 3 separate targets. 1 cannot be destroyed and can be shot at infinitely. The other 2 can be destroyed if shot once by an arrow. 5 arrows are fired. What are the odds that both destroy-able targets are destroyed? The destroyed targets cannot be shot at again.

 

[sadpwner]

Oh, I had a look over it and I have a question. For the 2nd part of your working out with the binomial probability. If you shoot a destroy-able target, you can't shoot at it again so the odds become 1/2 afterwards, so is your working out still right?

How about this one?
There are 3 separate targets. 1 can be destroyed if shot at 4 times but will end the game in doing so. The other 2 can be destroyed if shot once by an arrow. 5 arrows are fired. What are the odds that both destroy-able targets that are destroyed by one shot are destroyed? The destroyed targets cannot be shot at again. If the game is over, no more arrows can be shot.

Thanks btw

 

[braintic]

Is this question implying that you must hit one of the three targets?

 

[Drsoccerball]

Is this question implying that you must hit one of the three targets?

Not this again.

 

[braintic]

Not this again.

It's not really the same thing. It seems to be implying that every attempt to hit a target will succeed.

 

[sadpwner]

Is this question implying that you must hit one of the three targets?

yes it is...

I thought of another way to look at the question. Basically, you calculate the odds that 4 hit the undestroyable target and add it with the odds 3 hit the undestroyable, which equate to the same the odds that both of them are destroyed. Working it out now