$\"\"$

A success in this situation is a strike, so $\"\"$ and $\"\"$ .

Each frame represents a trial, so $\"\"$ .

Find the probability that Carol succeeds $\"\"$ times out of $\"\"$ trials :

So let $\"\"$ .

To find this probability, find the value of the term $\"\"$ in the expansion of $\"\"$ .

Where $\"\"$ and $\"\"$ .

Substitute the values $\"\"$ and $\"\"$ in the equation $\"\"$ .

$\"\"$ $\"\"$ .

$\"\"$

Therefore, the probability that Carol succeeds $\"\"$ times out of $\"\"$ trials is $\"\"$ .

$\"\"$

The probability that Carol succeeds $\"\"$ times out of $\"\"$ trials is $\"\"$ .