Probability of selling all 5 matchboxes vs. houses visited so far. Plot of cumulative distribution function of r>=5 successes after kth trial with p=0.4, with k<=30. Crosses 50% around 12th house and 90% around 18th house.
A barefoot girl warms herself on a snow-covered street. Illustration by Paul Hey
A #probability story problem: "The Little Match Girl"
Pat sells boxes of matches door to door, with a probability p = 0.4 of selling a box at each house. What's the chance she will exhaust all 30 houses in the village before selling the 5th box?
#NegativeBinomial #HCAndersen