Question 62

1. Determine total number of 2-digit integers:
   The 2-digit integers between 1 and 100 are $10, 11, 12, \dots, 99$.

   $$\text{Total 2-digit integers} = 99 - 10 + 1 = 90$$

2. Count 2-digit integers divisible by 7:
   The smallest 2-digit multiple of 7 is $7 \times 2 = 14$.
   The largest 2-digit multiple of 7 is $7 \times 14 = 98$.

   $$\text{Number of multiples of 7} = 14 - 2 + 1 = 13$$

3. Count integers not divisible by 7:

   $$\text{Favorable outcomes} = 90 - 13 = 77$$

4. Calculate probability:

   $$P(\text{not divisible by 7}) = \dfrac{77}{90}$$

This matches option (D).