A 3-digit number ranges from 100 to 999. We are considering 3-digit numbers that are multiples of 7. The smallest 3-digit multiple of 7 is $7 \times 15 = 105$. The largest 3-digit multiple of 7 is $7 \times 142 = 994$. The number of 3-digit multiples of 7 is $142 - 15 + 1 = 128$. This is our sample space size. We want the probability that such a number is also a multiple of 5. A number is a multiple of both 7 and 5 if it is a multiple of their least common multiple, LCM(7, 5) = 35. We need to find the number of 3- digit multiples of 35. The smallest 3-digit multiple of 35 is $35 \times 3 = 105$. The largest 3-digit multiple of 35 is $35 \times 28 = 980$. The number of 3-digit multiples of 35 is $28 - 3 + 1 = 26$. This is the number of favorable outcomes. The probability is the number of 3-digit multiples of 35 divided by the number of 3-digit multiples of 7: Probability = $26 / 128$. Simplifying the fraction: $26 / 128 = 13 / 64$.