In a free throw shooting contest...

Question

In a free throw shooting contest, you shoot free throws until you miss once or until you make four shots. You keep track of the sequence of misses/makes. How many outcomes are in the sample space for this experiment?

Answer 1

First, separate the rules:

  (a) shoot until you miss

  (b) shoot until you make 4 free-throws

They must be applied together.

 

Let 1 indicate a made free-throw and 0 indicate a miss.

 

So, to enumerate (that is, list them all), the ways you can shoot until you miss are:

0

10

110

1110

1111     (now rule (b) must be applied because you have made 4 free-throws)

 

That's 5 possible outcomes.

Answer 2

Start with the basic information:

  

  have to make 4 shots 

  can only miss 1 time

 

So, the total number of shots needed is 5.

 

I'm going to use 'p' (pass) for a made shot and 'F' (fail) for a missed shot.

 

'_' is an empty space that denotes a shot that was attempted.

 

 

So, you have 5 shots.   _ _ _ _ _

 

How many ways can you arrange 4 'p's and 1 'F' in those 5 slots? 

 

So,   F p p p p     first outcome

        p F p p p     second outcome

        p p F p p     third outcome

        p p p F p     fourth outcome

        p p p p F     fifth outcome

 

There are 5 outcomes possible in the sample space.