Question

A spinner is divided into 444 equal portions colored red, blue, green and yellow.
​


​If the spinner is spun, find the probability that it lands on:
Color
1
4
4
1
​

1
2
2
1
​

1
1
0
0
Red




Green




Blue or Yellow




Blue and Yellow

Answer 1

To find the probabilities, we will first determine the number of equal portions for each color on the spinner. Let's assume the distribution of colors is as follows (this is a common distribution, but you should adjust these numbers according to your specific spinner's layout if known):

- Red: 111
- Blue: 111
- Green: 111
- Yellow: 111

This distribution gives us a total of \( 444 \) equal portions (111 red + 111 blue + 111 green + 111 yellow = 444).

Now, let's compute the probabilities:

1. **Probability of landing on Red**:
\[
P(\text{Red}) = \frac{\text{Number of Red portions}}{\text{Total portions}} = \frac{111}{444} = \frac{1}{4}
\]

2. **Probability of landing on Green**:
\[
P(\text{Green}) = \frac{\text{Number of Green portions}}{\text{Total portions}} = \frac{111}{444} = \frac{1}{4}
\]

3. **Probability of landing on Blue or Yellow**:
\[
P(\text{Blue or Yellow}) = P(\text{Blue}) + P(\text{Yellow}) = \frac{111}{444} + \frac{111}{444} = \frac{111 + 111}{444} = \frac{222}{444} = \frac{1}{2}
\]

4. **Probability of landing on Blue and Yellow**:
- Since a spinner can land on only one color at a time, the probability of landing on both colors simultaneously is:
\[
P(\text{Blue and Yellow}) = 0
\]

In summary:

- **Probability of Red**: \(\frac{1}{4}\)
- **Probability of Green**: \(\frac{1}{4}\)
- **Probability of Blue or Yellow**: \(\frac{1}{2}\)
- **Probability of Blue and Yellow**: \(0\)