One-And-One Basketball Shots
Theoretical Probabilities Using Area Model

You should have completed and understood this worksheet. Be sure to see Mr. Beaty if you have any questions about the work here.

60% Shooter (60% = 60/100 = 6/10 = .6)
p(0) = .4
p(1) = .24
p(2) = .36
Most likely
Outcome = 0
Average points
per trip = .96
40% Shooter (40% = 40/100 = 4/10 = .4)
p(0) = .6
p(1) = .24
p(2) = .16
Most likely
Outcome = 0
Average points
per trip = .56
20% Shooter (20% = 20/100 = 2/10 = .2)
p(0) = .8
p(1) = .16
p(2) = .04
Most likely
Outcome = 0
Average points
per trip = .24
80% Shooter (80% = 80/100 = 8/10 = .8)
p(0) = .2
p(1) = .16
p(2) = .64
Most likely
Outcome = 2
Average points
per trip = 1.44

Make sure YOU determined and understand the results above. Then copy the results in the table below so that you can look for easy patterns in the numbers. This is why you will be able to answer quiz question easily and get them all correct.

Summary
Shooter's
Probability
Theoretical Probabilities Average points
per trip
0 points 1 point 2 points
20% = 2/10 = .2 .8 .16 .04 .24
40% = 4/10 = .4 .6 .24 .16 .56
60% = 6/10 = .6 .4 .24 .36 .96
80% = 8/10 = .8 .2 .16 .64 1.44
Below are the patterns we found in the numbers above. They are expressed as algebraic expressions (easy to remember and use). Be sure you see how to discover them in the numbers above and you learn them and how to use them for a quiz.
p 1-p p(1-p) p2 p + p2

After studying the above, be sure you paractice using your formulae correctly. Try to answer P(0), P(1), P(2), and the average points per trip for different shooters. Try a 50% shooter, a 75% shooter, and a 36% shooter. Try others and check with friends to see if you all get the same answers.