Using Table to Solve Probability Problems

Using Table to Solve Probability Example 1
A and B play a game, A throw a unbiased dice with number 1 - 6 on each side first, read the number on top side, then B throw it, read the number on top side, add these two number. if the sum is 8, A win. If the sum is 9, B win. Is the game fair?
Solution
solving probability problems
Using Table to Solve Probability Example 2
There are two red and three blue balls mixed together in a bag. All balls has the same size and same material. If you pick one, write down its color and put it back to bag. Shake the bag, then pick one again. What is the probability to pick two blue balls?
Solution
Let r1 is red1, r2 is red2, b1 is blue1, b2 is blue2, b3 is blue3. Note, if you get the red ball with number1 in first pick, after return it to bag, shake the bag, you may have the chance to pick it again. This is the reason that r1 r1 is one of the all outcomes. The number of all possible outcomes is 25, the number of ways to pick two blue balls is 9.
solving probability problems
Using Table to Solve Probability Example 3
There are three red cards with number 1- 3 on each, and two black cards with number 1 - 2 on each, mixed together in a box. All cards has the same size and material. If you pick two cards, what is the probability that both cards have number 2?
Solution
Let r1 is red1, r2 is red2, r3 is red3, b1 is black1, b2 is black2. Note, since you do not return the first card you picked, so you never get the same card in second pick. The number of all possible outcomes is 20, There are two ways to get two cards that each has number two, which are ( r2, b2 ) and ( b2 , r2 )
solving probability problems