An unknown number of ping pong balls have been numbered $$ 1,2,3 $$, and so on. The probability of randomly selecting a prime number when drawing a ping pong ball is $$ \frac{3}{10} $$. If the highest prime number used was 37 , how many balls are there?

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To determine the total number of ping pong balls, let's follow these steps:

1. **Identify the Primes up to 37:**
   The prime numbers between 1 and 37 are:
   $$
   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
   $$
   There are **12 prime numbers** in this range.

2. **Set Up the Probability Equation:**
   The probability of selecting a prime number is given as:
   $$
   \frac{\text{Number of Primes}}{\text{Total Number of Balls}} = \frac{3}{10}
   $$
   Plugging in the number of primes:
   $$
   \frac{12}{N} = \frac{3}{10}
   $$

3. **Solve for $$ N $$:**
   Cross-multiplying gives:
   $$
   12 \times 10 = 3 \times N \implies 120 = 3N \implies N = 40
   $$

4. **Verification:**
   - The highest prime used is 37, and since $$ N = 40 $$, all primes up to 37 are included.
   - The next prime after 37 is 41, which is greater than 40, ensuring that 37 is indeed the highest prime number in the set.

**Therefore, there are 40 ping pong balls.**

**Answer:** 40
There are 40 ping pong balls.

An unknown number of ping pong balls have been numbered \( 1,2,3 \), and so on. The probability of randomly selecting a prime number when drawing a ping pong ball is \( \frac{3}{10} \). If the highest prime number used was 37 , how many balls are there?

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