Answer:
2/5 or 0.4, which is also equivalent to a 40% chance.
Explanation:
To determine the theoretical probability of drawing a prime number from the numbers 2 through 16, we need to first identify the prime numbers in this range. The prime numbers between 2 and 16 are 2, 3, 5, 7, 11, and 13.
There are a total of 15 numbers in the hat, and 6 of them are prime. Therefore, the probability of drawing a prime number can be calculated as:
Probability of drawing a prime number = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes = 6 (since there are 6 prime numbers in the range of 2 through 16)
Total number of possible outcomes = 15 (since there are 15 numbers in the hat)
So, the probability of drawing a prime number is:
Probability of drawing a prime number = 6 / 15
Simplifying this fraction by dividing both numerator and denominator by 3, we get:
Probability of drawing a prime number = 2 / 5
Therefore, the theoretical probability of drawing a prime number from the numbers 2 through 16 is 2/5 or 0.4, which is also equivalent to a 40% chance.