1. Take any number n from all 3-digit positive integers and find the probability that the logarithm of this number with base 2 is also a positive integer.

All three digits are * * *: 900.

The logarithm with base 2 is also a positive integer with only three digits:128,256,512.

Probability: 3/900= 1/300

2. Take any number from all two digits (10-99) and find the probability that this number can be divisible by 2 or 3.

All two digits * * *: 90.

Number of multiples of 2 in a two-digit number: [99/2]-[9/2]=45.

Number of multiples of 3 in two digits: [99/3]-[9/3]=30.

Number of multiples of 6 in two digits: [99/6]-[9/6]= 15.

Number of multiples of 2 or 3 of two digits: 45+30- 15=60.

Probability: 60/90=2/3