FINITE MATH HOMEWORK

Question

In a free throw shooting​ contest, you shoot free throws until you miss once or until you make

seven shots. You keep track of the sequence of​ misses/makes. How many outcomes are in the sample space for this​ experiment?

Answer 1

The valid outcomes include any sequence of up to and including seven "makes" (I'll use "1" for each) or any single "miss" (I'll use "0" for that).

Then possible sequences for the shots are

0, 10, 110, 1110, 11110, 111110, 1111110,1111111.

Again, by the rule, any 0 stops the game, any 1 and shoot again, until seven Ones. So these are the only possibilities.

The size of the sample space is then EIGHT.