Question 1155820: an experiment is performed where a 6-sided die is rolled and then a 3-color spinner is spun. the possible outcomes for each event are 1,2,3,4,5 and 6 for the 6-sided die and red (r), blue (b), and yellow (y) for the 3-color spinner. identify the sample space for this experiment
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
The sample space is the set of all pairs (n,L),
where "n" is any integer number from 1 to 6 inclusive, and L is any of the tree letters "r", "b", "y".
So, the sample space in this case consists of 6*3 = 18 elements, each having the probability  .
Answered, explained, solved and completed.
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For introductory lessons on Elementary Probability theory see the lessons
- Simple and simplest probability problems
- Solving probability problems using complementary probability
- Elementary Probability problems related to combinations
- A True/False test
- A multiple choice answers test
- Conditional probability problems
- Typical probability problems from the archive
- Experimental probability problems
- Elementary operations on sets help solving Probability problems
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Solved problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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Happy learning (!)
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
Outcomes of the die roll = {1,2,3,4,5,6}
Colors on the spinner = {R, B, Y} (for red, blue, yellow)
There are 6 items in the first set, and 3 items in the second, so 6*3 = 18 items total in the sample space.
Imagine we had a 6 by 3 table.
6 rows and 3 columns
The 6 rows is from the 6 values in {1,2,3,4,5,6}
The 3 columns is from the 3 values in {R, B, Y}
Along the top and left side, list the values mentioned to get this table so far
Now fill in the table by writing the proper letter and number combination. For instance, in row 3, column 2, we will have B3 since "B" is in column 2 and "3" is in row 3. Getting the outcome B3 tells the reader the spinner landed on blue while the die landed on 3. Fill the other 17 cells in a similar fashion and you'll end up with this:
| R | B | Y |
| 1 | R1 | B1 | Y1 |
| 2 | R2 | B2 | Y2 |
| 3 | R3 | B3 | Y3 |
| 4 | R4 | B4 | Y4 |
| 5 | R5 | B5 | Y5 |
| 6 | R6 | B6 | Y6 |
Each of the 18 items inside the table refer to an outcome in the sample space. For instance R2 means the spinner landed on red and the die rolled to a "2".
If you were to erase the table lines and the outer headers, adding in curly braces around the entire thing, then you'd end up with this final sample space
{
R1, B1, Y1,
R2, B2, Y2,
R3, B3, Y3,
R4, B4, Y4,
R5, B5, Y5,
R6, B6, Y6
}
Normally when writing out a set, you write it all as one single line; however, I broke up the set into 6 lines just like how the table is laid out.
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