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 can you help me?

Answer 2

4 misses will do it
3 misses and a half-way will do it
that's about it
what is the P?

Answer 3

there is only 1 way to miss 4 times


and they its how many ways can half in and 3 misses occur...

that would give you the total number of sequences for not hammering the nail all the way in..

Answer 4

@telliott99 How would i find P?

Answer 5

As @campbell_st says there is only one way to miss four times so
P = (1/4)^4 = 1/256
As for the other, there are four ways to hit half-way once in four times so
P = 4 (1/4) (1/4)^3 = 4/256.

Answer 6

would you then add thos up to get 5/256

Answer 7

@telliott99 would you then add them up to get 5/256?

Answer 8

@telliott99 Are you still here?

Answer 9

Yes.

Answer 10

@telliott99 do i add both up to get 5/256

Answer 11

My yes was yes, add them up.

Answer 12

I got it wrong for some reason.