Question

Negative Binomial experiment is based on sequences of Bernoulli trials with probability

of success p. Let x+m be the number of trials to achieve m successes, and then x has a

negative binomial distribution. In summary, negative binomial distribution has the

following properties



Each trial can result in just two possible outcomes. One is called a success and

the other is called a failure.



The trials are independent



The probability of success, denoted by p, is the same on every trial.



The experiment consists of m successes, and x+m repeated trials, and the m

th

success occurs at the (x+m)

th

trial.

1. Write down the probability distribution P(x=k), consistent with the notation here

2. If you are tossing a regular coin repeatedly, what is the probability that the 3

rd

head occurs at the 6

th

time you toss it?

3. Anne is selling girl scot cookies in her neighborhood with 20 houses. She has a

target to sell 10 boxes. Suppose each house has a probability 0.6 to buy one box

of her cookies. What is the probability that she sells the last box at the 15

th

house? What is the probability that she exhausts all 20 houses?

Answer 1