Question
An unknown number of ping pong balls have been numbered
prime number when drawing a ping pong ball is
highest prime number used was 37 , how many balls are
there?
prime number when drawing a ping pong ball is
highest prime number used was 37 , how many balls are
there?
Ask by Newton Nguyen. in the Philippines
Jan 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 40 ping pong balls.
Solution
To determine the total number of ping pong balls, let’s follow these steps:
-
Identify the Primes up to 37:
The prime numbers between 1 and 37 are:There are 12 prime numbers in this range. -
Set Up the Probability Equation:
The probability of selecting a prime number is given as:Plugging in the number of primes: -
Solve for
:
Cross-multiplying gives: -
Verification:
- The highest prime used is 37, and since
, 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.
- The highest prime used is 37, and since
Therefore, there are 40 ping pong balls.
Answer: 40
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the total number of ping pong balls, let’s start by identifying the prime numbers up to 37. The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37. This gives us 12 prime numbers.
If the probability of selecting a prime number is
Substituting in the number of primes:
To solve for
This leads to:
Dividing both sides by 3 gives:
Thus, there are 40 ping pong balls in total.
