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 number selected is odd if you know it is prime, we first need to determine the number of possible outcomes and the number of favorable outcomes.
First, let's determine the number of prime numbers among 1 to 9. The prime numbers in this range are 2, 3, 5, and 7. So, there are 4 prime numbers.
Now, let's find the number of prime numbers that are odd. Among the prime numbers we listed earlier, 3 and 7 are odd. Therefore, there are 2 prime numbers that are odd.
Hence, the probability that the number selected is odd if it is prime can be calculated as the number of favorable outcomes (prime odd numbers) divided by the number of possible outcomes (prime numbers):
Probability = Number of favorable outcomes / Number of possible outcomes
= 2 / 4
= 1/2
= 0.5
Therefore, the probability of selecting an odd number if you know it is prime is 0.5 or 50%.