 10) There are two boxes and tokens numbered from 1 to 4 are put in each box. If one token is taken from each 
box, what is the probability that the sum of the numbers written on the tokens is a prime number

We have two boxes, each containing tokens numbered from 1 to 4. One token is drawn from each box, and we want to find the probability that the sum of the numbers on the two tokens is a prime number.

### Step 1: List all possible outcomes
The numbers on the tokens in each box are \( 1, 2, 3, 4 \). The total number of possible outcomes when drawing one token from each box is:

\[
\text{Total outcomes} = 4 \times 4 = 16
\]

We now list all possible pairs of token sums:

- From box 1: \( 1 \), from box 2: \( 1 \), sum = \( 1+1 = 2 \) (prime)
- From box 1: \( 1 \), from box 2: \( 2 \), sum = \( 1+2 = 3 \) (prime)
- From box 1: \( 1 \), from box 2: \( 3 \), sum = \( 1+3 = 4 \) (not prime)
- From box 1: \( 1 \), from box 2: \( 4 \), sum = \( 1+4 = 5 \) (prime)

- From box 1: \( 2 \), from box 2: \( 1 \), sum = \( 2+1 = 3 \) (prime)
- From box 1: \( 2 \), from box 2: \( 2 \), sum = \( 2+2 = 4 \) (not prime)
- From box 1: \( 2 \), from box 2: \( 3 \), sum = \( 2+3 = 5 \) (prime)
- From box 1: \( 2 \), from box 2: \( 4 \), sum = \( 2+4 = 6 \) (not prime)

- From box 1: \( 3 \), from box 2: \( 1 \), sum =

There are two boxes and tokens numbered from 1 to 4 are put in each box. If one token is taken from each box, what is the probability that the sum of the numbers written on the tokens is a prime number?

Explore how to calculate the probability that the sum of numbers drawn from two boxes of tokens is a prime number. This problem involves probability theory, number theory, and understanding prime numbers, making it suitable for students in Grades 6-8.

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