Question

When I swing at a nail, I drive it all the way in with probability 1/2. With probability 1/4, I hit it half-way in, and with 1/4 probability I miss it entirely. I'm pretty sure that if I swing 4 times at a nail, I'll get it all the way in almost all the time. Let's see if I'm right.

How many sequences of 4 swings could leave the nail still not knocked all the way in?

Answer 1

@telliott99 I need help with this again, I got the answer wrong.

Answer 2

Show me what you have.

Answer 3

We did it yesterday and got 5/256 because of..

Answer 4

that's all i have

Answer 5

can you teach me how to do this?

Answer 6

Well, maybe I was wrong, let's see.

Answer 7

ok

Answer 8

I'm not sure I see a simpler way to do this. There are 4 steps with 3 possibilities at each step. That's a lot. Each path has a probability that is the product of the individual steps..

Answer 9

We thought about it the other way around, which specific steps would leave the nail still poking up.

Answer 10

Like 4 misses in a row is 1/4 1/4 1/4 1/4 = 1/256
A half-hit on the first attempt is 1/256 as well, but the half-hit could be on any of the 4 steps so that's 4/256.

Answer 11

Yes

Answer 12

Any sequence with 2 half-hits or a whole hit is all the way down.

Answer 13

So I still like our answer, I guess.

Answer 14

hmm.. tricky problem

Answer 15

Yes. Put it out there again, and maybe ask someone else for help. Sorry.

Answer 16

@Zarkon Can you help me?

Answer 17

@Zarkon Are you there?