Question

A bag contains five ping-pong balls numbered 1 to 5. Two balls are removed to form a two digit number. The smallest possible number is 12 and the largest is 54. What is the probability that the number formed is prime? (hint: Write out the entire sample space)

Answer 1

Answer:

$\frac{11}{42}$ or 26.19%

Step-by-step explanation:

If the range of possible numbers is between 12 and 54 then that means that there are 42 (54 - 12) possible numbers that can be made. In this range, there are 11 prime numbers which are the following...

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53

Therefore, the probability that the number formed is a prime would be $\frac{11}{42}$ which if we divide and multiply the decimal by 100 we get the probability in percentage form.

$\frac{11}{42}$ = 0.2619

0.2619 * 100 = 26.19%

Finally, we can see that the probability of this happening is 26.19%