Question

When shooting two free throws, if a Red Devil basketball player makes her first free throw, there is a 85% chance that she will make her second free throw. If she misses her first free throw, there is only a 55% chance that she will make her second free throw. Suppose the chance she makes her first free throw is 55%, DRAW A TREE DIAGRAM IN YOUR NOTES AND USE IT TO HELP YOU SOLVE THIS PROBLEM.What is the probability that: a) She makes both free throws? b) She misses both free throws? c) She makes exactly one of the two free throws? d) She makes at least one of the free throws?

Answer 1

1) Gathering the data

55%First Free throw success - 2nd Free throw (success 85%)

First F.T. (failure) - 2nd F.T. (sucess 55%)

Suppose 1st free throw = 55%

2) Let's look at the tree and answer it:

a) She makes both free throws?

If She does, we can multiply 0.55 x 0.85 = 0.4675 or 46.75%

b)She misses both free throws?

If She loses then, we can multiply 0.45 x 0.45 = 0.2025 or 20.25%

c) She makes exactly one of the two free throws?

Let's pick the probabilities of success and failure and then add them

(0.55 x 0.15 + 0.45 x 0.55 = 0.0825 x 0.2475= 0.02041 or 2.04%

d) She makes at least one of the free throws?​

In this case, let's subtract, 1 - ( all the free throws that she couldn't make it. Then we'll have

1 - ( 0.45 x 0.45) = 0.7975 or 79.75%