There would be 65 doses in a 13 ounce bottle.
The probability is 0.0008.
I used a binomial probability on this one, since there are two outcomes (either pass or fail); the events are independent (the probability of one person passing does not influence the probability of another passing); and there are a fixed number of trials (in this case, 20).
For binomial probabilities, we use the formula:

With our information, we have:
The associative law states that it doesn't matter how we group numbers when we add and/or multiply. So we could rearrange the brackets and parentheses to get the equivalent equation:
9m(6+n)
Both equations total:
54m+9mn
(I applied the distributive property to solve it).