A vending machine has marbles of 4 different colors: Red, blue, purple,and yellow. The marbles are well mixed. You drop a quarter into the machine and you get 2 random marbles. Write out the sample space for the experiment. The sample space should be N = 10.
To determine the sample space for this experiment, we need to consider all possible outcomes. Since there are 4 different colored marbles and you are getting 2 marbles, we can calculate the number of possible outcomes by using combinations.
The formula for combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items and r is the number of items we are choosing.
In this case, n = 4 (4 different colored marbles) and r = 2 (2 marbles chosen). So, the number of possible outcomes is:
C(4, 2) = 4! / (2! * (4-2)!)
= 4! / (2! * 2!)
= 24 / (2 * 2)
= 24 / 4
= 6
Hence, there are 6 possible outcomes when choosing 2 marbles from 4 different colors (Red, blue, purple, and yellow). Now, let's list out all the possible outcomes:
1. Red - Blue
2. Red - Purple
3. Red - Yellow
4. Blue - Purple
5. Blue - Yellow
6. Purple - Yellow
So, the sample space for this experiment, with N = 10, is: {Red-Blue, Red-Purple, Red-Yellow, Blue-Purple, Blue-Yellow, Purple-Yellow}.