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 =