Homework/Probability/VERY CONFUSED PLEASE HELP

Question

An urn contains a total of 9 marbles out of which 2 are red, 3 are white and the remaining are blue. Two marbles are drawn out of the urn in succession.What is the probability that both marbles are the same color if:

 

a. Replacement is allowed?

 

 

b. The first marble is not replaced?

Answer 1

For simple probability problems the answer is found by determining the number of possible successfully outcomes as compared to the number of total possible outcomes.  In the first pick, if you pick a red marble then there are two marbles possible with a replacement and only one other marble that is red without replacement, and the other seven marbles will not give you a match,  If you first pick a white marble then there are three possible chances with replacement, two other chances for a match without replacement, and six marbles that will not match.  For the blue marbles, there are four possible matches with a replacement, three without replacement, and five marbles that will not match.  

 

Now let's do the math:

 

Replacement allowed:

There are a total of 9 possible picks each time so that is 9x9 or 81 possible outcomes.  

 

2/9 x 2/9 (Red) + 3/9 x 3/9 (White) + 4/9 x 4/9 (Blue) = 4/81 + 9/81 + 16/81   = 29/81  or 35.8% chance of a match of the same color

 

No replacement allowed:

 

9 possible first picks and 8 possible second picks for 9x8 = 72 possible outcomes

 

2/9 x 1/8 (Red) + 3/9 x 2/8 (White) + 4/9 x 3/8 (Blue) = 2/72 + 6/72 + 12/72 = 20/72 or 27.8% chance of a match of the same color