00:01
Hey there, welcome to numerate.
00:03
We have a manufacturer of clothing looking at the probability of a button flaw, which is 0 .0 ,004, and we are examining 58 shirts, each with five buttons.
00:20
So we're approximating here with a person probability model.
00:24
So we are going to be taken the probability, multiplied by the number of shirts.
00:30
And each one has five, so we multiply by five, giving us a lambda value of 1 .16.
00:38
So this would be our average here, in which we're going to use to plug into our prasun equation, which is the probability of x, equaling e raised to our constant, or our constant raised to the negative lambda, times lambda raised to the x, divided by x factorial.
01:00
So for our first one here, part a, we're basically looking for the probability of zero flaws.
01:08
So hence, what we have here is e raised to 1 .16 times 1 .16 raised to 0 divided by 0 factorial, given us a probability that equals around 0 .313.
01:29
All right, so let's try part b here.
01:34
What is the probability that she finds at least one? the x is at least one, which is going to be equivalent to 1 minus the probability that x is less than 1...