Question

A box contains 6 blue balls and 8 green balls.

a) You sample 5 balls from this box, with replacement. Let X be the number of blue balls in the sample. What is the name of the distribution of X? specify the parameters.

b) Find P(X >= 2)

c) You sample 5 balls from this box, without replacement. Let Y be the number of blue balls in the sample. What is the name of the distribution of Y. Specify the parameters.

d) Find P(Y =< 2)

Answer 1

a) this is binomial distribution with parameters , n=5 and p=probability of blue ball =6/14 =3/7

b)

probability =

P(X>=2)=

1-P(X<=1)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.7106

c)

this is hypergeometric distribution with parameters:

sample size n=				5
population size(total balls) N=				14
success population size (blue balls) k=				6

d)

probability =

P(Y<=2)=

∑x=0y     (kCy)(N-kCn-y)/(NCn) =

0.6573