The negative binomial distributionEdexcel A-Level Further Maths: Mind map

Exam questions on The negative binomial distribution

1. A shooter hits the target with probability $0.3$ on each shot, independently of all other shots. Let $X$ be the number of shots needed to score $3$ hits, so that the third hit occurs on shot $X$.
   Find the probability that the third hit is scored on or before the fourth shot.2 marks
2. A fair six-sided die is rolled repeatedly. Let $X$ be the number of rolls up to and including the roll on which the second six appears.
   Find the probability that more than $3$ rolls are needed to obtain the second six.2 marks
3. A telesales agent makes a sale on each call with probability $0.25$, independently of all other calls. Let $X$ be the number of calls made up to and including the call on which the fourth sale is made.
   State the distribution of $X$, and find $\mathrm{E}(X)$ and $\mathrm{Var}(X)$.3 marks