Suppose that a natural number from 1 through 9 is selected at random. What is the probabiliy that the number selected is odd if you know that it is prime?

To find the probability that the selected number is odd given that it is prime, we need to determine the number of favorable outcomes (odd prime numbers) and divide it by the total number of possible outcomes (prime numbers).

In this case, we know that the prime numbers between 1 and 9 are 2, 3, 5, and 7. Let's analyze each of these numbers to determine if they are odd or even.

2 is the only even prime number, so it does not satisfy the condition of being odd.

On the other hand, 3, 5, and 7 are odd prime numbers.

Now, the total number of prime numbers is 4, and the number of odd prime numbers is 3.

To find the probability, we divide the number of odd prime numbers by the total number of prime numbers:

Probability = Number of odd prime numbers / Total number of prime numbers
Probability = 3 / 4

Therefore, the probability that the selected number is odd, given that it is prime, is 3/4 or 0.75, which can also be expressed as 75%.