The problem has a rather small sample space.
It is easier to simply LIST the outcomes.
The first number is a 3.Two digits are chosen at random from a table of random numbers
. . containing digits: 0, 1, 2. ... 9.
Find the probability that
(a) the sum of the two digits is greater than 9, given that the first number is 3
Sample space: . . . . 10 outcomes
The sum is greater than 9: . . . . 3 outcomes.
The sum is greater than 8.(b) the second number is 2, given that the sum of the two munber is greater than 7
Sample space: . . . . 64 outcomes
The second number is 2: . . . . 4 outcomes.
Difference of the numbers is 4.(c) the first number is 4, given that the difference between the two numbers is 4.
Sample space: . . . . 12 outcomes
First number is 4: . . . . 2 outcomes