Just doing some practice questions on probability and got stuck on a few of them:
Q1: Roll one die. Stop a the 4th roll or when a 6 appears (whichever occurs first). Let X be the number of rolls. Find the pmf, expectation and variance of X.
I know how to calculate these things. It's just formulating a table of values that I'm struggling with here so any advice would be welcome.
Q2: To check the quality if drainpipes a manufacturer slects 10 pipes at random from each large production batch and subjects them to an impact test. Flawed pipes break on the test but good ones don't. If more than 2 pipes on the test break, the whole batch is scrapped.
What is the probablity that the batch will be scrapped when 10% of the pipes in it are flawed?
Here i know that P(batch is scrapped) = 0.2
Is this therefore some sort of conditional probability question? Any hints to get me started again would be welcome