From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997

A Dice Free Probability Worksheet

This worksheet contains some interesting probability problems - and none of them involve coins, dice, cards, marbles or urns.

1. When fouled without possession of the ball, a basketball player is awarded 'one-and-one'. This means that the player gets a free shot, and if they are successful they are given a second free shot. Each successful free shot earns one point, so a player would score 0 points if they miss the first shot, 1 point if they make the first shot and miss the second or 2 points if they make both shots.

For the following questions, assume that the probability that a particular player makes a shot is p, and that the events 'making the first shot' and 'making the second shot' are independent. A very poor shooter (with a value of p close to 0) is most likely to score to score 0 points, while a very good shooter (with a value of p close to 1) is most likely to score 2 points.

a. One point is NEVER the most likely outcome. Show that the probability of scoring 1 point can never exceed 1/4 and find the value of p for which this occurs.

b. What value of p makes it equally likely that a player scores 0 or 2 points in a one-and-one situation?

Thanks to Pat Ballew for this neat question.