Suppose you randomly choose a number between 1 and 20. what are the odds against choosing a prime number?

Hint: P(prime number) = Number of primes from 1 to 20/Number of numbers from 1 to 20

we have three things to consider: success, failure, total
we can create a chart for these as

S . . . . F . . . . T
8 . . . . 12 . . . 20
odds in favor are success / failure so we get
8/12 = 2/3

The answer would be 7 cages