Basketball free throw question

Question

In basket ball you can be awarded a two shot free throw attempt. You are given two shots from the free throw line and each shot you make is worth 1 point. This allows you to earn zero, one or two points, in any two shot free throw attemp. Shelly is a very streaky shooter. When she attempts her first free throw she has an 80% of making it. If she makes her first shot, her confidence goes up and she has a 90% chance of making her second shot. If she misses her first shot her confidence goes down and she only has a 60% chance of making her second shot. If Shelly is given 100 two shot free throw attempts,how many points will she score?

Answer 1

The probability that Shelly makes both shots is (80%)*(90%) = 0.8*0.9 = 0.72, so the probability that Shelly earns 2 points in any given two shot free throw attempt is 0.72 = 72%.

 

The probability that Shelly makes the first shot, but misses the second shot is (80%)*(1 - 90%) = (80%)*(10%) = 0.8*0.1 = 0.08, and the probability that Shelly misses the first shot, but makes the second shot is (1 - 80%)*(60%) = (20%)*(60%) = 0.2*0.6 = 0.12, so the probability that Shelly earns 1 point in any given two shot free throw attempt is 0.08 + 0.12 = 0.2 = 20%.

 

The probability that Shelly misses both shots is (1 - 80%)*(1 - 60%) = (20%)*(40%) = 0.2*0.4 = 0.08, so the probability that Shelly earns 0 points in any given two shot free throw attempt is 0.08 = 8%.

 

Now, the expected value of the number of points Shelly earns in any given two shot free throw attempt is 2*0.72 + 1*0.2 + 0*0.08 = 1.64. Thus, if she is given 100 attempts, we can expect her to score 100*1.64 = 164 points.