+1836 1. 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. Hitting it half-way in twice will drive it all of the way in. 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?
2. 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. What is the probability I fail to get the nail driven completely in?
+33661 1. There are 5 sequences of four swings that would fail to get the nail knocked all the way in. They are:
(miss miss miss miss) prob = (1/4)4
(halfway miss miss miss) prob = (1/4)4
(miss halfway miss miss) prob = (1/4)4
(miss miss halfway miss) prob = (1/4)4
(miss miss miss halfway) prob = (1/4)4
2. Overall probability = 5*(1/4)4 = 5/256
.
+33661 1. There are 5 sequences of four swings that would fail to get the nail knocked all the way in. They are:
(miss miss miss miss) prob = (1/4)4
(halfway miss miss miss) prob = (1/4)4
(miss halfway miss miss) prob = (1/4)4
(miss miss halfway miss) prob = (1/4)4
(miss miss miss halfway) prob = (1/4)4
2. Overall probability = 5*(1/4)4 = 5/256
.
