There is total batch of 100 products. 10 of the products are faulty. 2 products are taken randomly

Question

There is total batch of 100 products. 10 of the products are faulty. 2 products are taken randomly from the batch without replacement for them. Variable X is the total number of faulty products selected.

a) Create a probability distribution chart for X?

b) Calculate E(X)E(X), the expected value for X ?

I have tried to represent this by a binomial distribution.

P(0)=2C0∗(0,1)0∗(0,9)2=0,81P(0)=2C0∗(0,1)0∗(0,9)2=0,81
P(1)=2C1∗(0,1)1∗(0,9)1=0,18P(1)=2C1∗(0,1)1∗(0,9)1=0,18
P(2)=2C2∗(0,1)2∗(0,9)0=0,01P(2)=2C2∗(0,1)2∗(0,9)0=0,01
so probability distribution for X

x 0 1 2
---------------------------
p 0,81 0,18 0,01

 

and expected value for X.

E(X)=x1∗p1+x2∗p2+x3∗p3

E(X)=0∗0,81+1∗0,18+2∗0,01=0,2

Right answer for E(X) is 0,2011. Can't get it.

Answer 1

expected value = mean = np = 10(.10) = 1 defective in sample of 10 of the 100

select 2 without replacement

1/10 chance 1st is defect, 9/99 = 1/11 chance 2nd is a defect

chance both are defects = .(1/10)(1/11) = 1/110

expected value of x = 10/110 = 1/11

you get 1 for mean of 1 selection

then np = 9(9/99= 9/11 = expected number of defects on 2nd selection

1 9/11 = exp(x) for 2 selections