Question
blue, and yellow. The spinner is spun two times. Use R to represent red, G to represent green, B to represent blue, and Y to represent yellow. What is the sample space of this probability experiment?(1 point)
Responses
S={R, G, B, Y}
cap s is equal to R, G, B, Y
S={RR, RG, RY, GG, GB, GY, BB, BY, YY }
cap s is equal to RR, RG, RY, GG, GB, GY, BB, BY, YY
S={RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY}
cap s is equal to RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY
S={RG, RB, RY, GR, GB, GY, BR, BG, BY, YR, YG, YB}
Responses
S={R, G, B, Y}
cap s is equal to R, G, B, Y
S={RR, RG, RY, GG, GB, GY, BB, BY, YY }
cap s is equal to RR, RG, RY, GG, GB, GY, BB, BY, YY
S={RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY}
cap s is equal to RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY
S={RG, RB, RY, GR, GB, GY, BR, BG, BY, YR, YG, YB}
Answers
GPT-4o mini
To calculate the sample space for spinning a spinner that can land on four colors (Red, Green, Blue, Yellow) two times, we need to list all the possible outcomes of the two spins. Each spin has four possible outcomes, and because the spins are independent, we can find the total number of outcomes by combining each outcome of the first spin with each outcome of the second spin.
Let’s denote:
- R = Red
- G = Green
- B = Blue
- Y = Yellow
For each spin, we have the following possible outcomes: R, G, B, Y.
When the spinner is spun two times, the sample space \( S \) includes all ordered pairs of the outcomes from each spin. These outcomes can be represented as follows:
1. RR (Red then Red)
2. RG (Red then Green)
3. RB (Red then Blue)
4. RY (Red then Yellow)
5. GR (Green then Red)
6. GG (Green then Green)
7. GB (Green then Blue)
8. GY (Green then Yellow)
9. BR (Blue then Red)
10. BG (Blue then Green)
11. BB (Blue then Blue)
12. BY (Blue then Yellow)
13. YR (Yellow then Red)
14. YG (Yellow then Green)
15. YB (Yellow then Blue)
16. YY (Yellow then Yellow)
Thus, the complete sample space \( S \) can be represented as:
\[
S = \{ RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY \}
\]
Among the given options, the correct representation of the sample space is:
**S = {RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY}**
Therefore, the correct choice is:
**S={RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY}**
Let’s denote:
- R = Red
- G = Green
- B = Blue
- Y = Yellow
For each spin, we have the following possible outcomes: R, G, B, Y.
When the spinner is spun two times, the sample space \( S \) includes all ordered pairs of the outcomes from each spin. These outcomes can be represented as follows:
1. RR (Red then Red)
2. RG (Red then Green)
3. RB (Red then Blue)
4. RY (Red then Yellow)
5. GR (Green then Red)
6. GG (Green then Green)
7. GB (Green then Blue)
8. GY (Green then Yellow)
9. BR (Blue then Red)
10. BG (Blue then Green)
11. BB (Blue then Blue)
12. BY (Blue then Yellow)
13. YR (Yellow then Red)
14. YG (Yellow then Green)
15. YB (Yellow then Blue)
16. YY (Yellow then Yellow)
Thus, the complete sample space \( S \) can be represented as:
\[
S = \{ RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY \}
\]
Among the given options, the correct representation of the sample space is:
**S = {RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY}**
Therefore, the correct choice is:
**S={RR, RG, RB, RY, GR, GG, GB, GY, BR, BG, BB, BY, YR, YG, YB, YY}**