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=0}^{x-1 }
(_{n}C_{x})p^{x}(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=0}^{y }
(_{k}C_{y})(_{N-k}C_{n-y})/(_{N}C_{n})
= |
0.6573 |

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