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.

Question

What is the probability I fail to get the nail driven completely in?

Answer 1

paoeiwurnv

Answer 2

A company has three machines A, B and C which all produce the same two parts, X and
Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and
machine C produces the rest. 40% of the parts made by machine A are part X, 50% of the
parts made by machine B are part X, and 70% of the parts made by machine C are part X.
A part produced by this company is randomly sampled and is determined to be an X part.
With the knowledge that it is an X part, find the probabilities that the part came from
machine A, B or C

Answer 3

A company has three machines A, B and C which all produce the same two parts, X and
Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and
machine C produces the rest. 40% of the parts made by machine A are part X, 50% of the
parts made by machine B are part X, and 70% of the parts made by machine C are part X.
A part produced by this company is randomly sampled and is determined to be an X part.
With the knowledge that it is an X part, find the probabilities that the part came from
machine A, B or C