I've been working through a problem set covering the various probability distributions and I seem to be getting all of them right except certain questions regarding the negative binomial.
For example,
You have a bowl that contains 2 pennies, 4 nickels and 6 quarters. You take out a coin at
random and replace it. You do this repeatedly.
(a) Calculate the probability that you will observe 4 non-nickels before the 3rd nickel.
My thinking is:
You can draw 4 non nickels right away (totaling 4 trials), draw 4 non nickels with 1 nickel (totaling 5 trials), draw 4 non nickels with 2 nickels (totaling 6 trials).
Letting X= RV number of trials it takes to get 4 non nickels
P(4)=(8/12)^4
P(5)=(4c3)(4/12)(8/12)^4
P(6)=(5c3)(4/12)^2 (8/12)^4
Adding these probabilities up and I do not get the correct answer. The correct answer is .1097. Could anyone give me some pointers or a hint in the right direction? Thanks!
For example,
You have a bowl that contains 2 pennies, 4 nickels and 6 quarters. You take out a coin at
random and replace it. You do this repeatedly.
(a) Calculate the probability that you will observe 4 non-nickels before the 3rd nickel.
My thinking is:
You can draw 4 non nickels right away (totaling 4 trials), draw 4 non nickels with 1 nickel (totaling 5 trials), draw 4 non nickels with 2 nickels (totaling 6 trials).
Letting X= RV number of trials it takes to get 4 non nickels
P(4)=(8/12)^4
P(5)=(4c3)(4/12)(8/12)^4
P(6)=(5c3)(4/12)^2 (8/12)^4
Adding these probabilities up and I do not get the correct answer. The correct answer is .1097. Could anyone give me some pointers or a hint in the right direction? Thanks!
Questions on setting up negative binomial
