Question

A baseball player comes up to bat 3 times during a league game. He either gets a hit or gets an out. How many different combinations are there for the three at bats? Make a tree diagram to help see the situation.

Answer 1

8 different combinations are possible.

Explanation:

Here, we have 2 different combinations for each time.

And the player comes out to bat 3 times.

So, total number of combinations are:

`2^(3)` i.e. a total of 8 number of times.

Let a hit is termed as 'H' and an out is termed as 'O'.

Total combinations are:

{HHH, HHO, HOH, HOO, OHH, OHO, OOH, OOO}

Kindly have a look at the tree diagram attached in the answer area.

In starting, there are 2 combinations possible, i.e. 'O' and 'H'.

After 'O' , 2 possible i.e. 'O' and 'H'.

After 'H' , 2 possible i.e. 'O' and 'H'.

and so on....