Carol makes a spinner for a game. The spinner is divided into 10 equal sections. Each section is shaded 1 of these colors: green, red, yellow, or blue. On this spinner, the probability of spinning green is 3 times as great as the probability of spinning red. The probability of spinning red is twice as great as the probability of spinning blue. The number of yellow sections is equal to the number of blue sections. How many sections of each color are there? What is the probability of spinning each color?

Question

Carol makes a spinner for a game. The spinner is divided into 10 equal sections. Each section is shaded 1 of these colors: green, red, yellow, or blue. On this spinner, the probability of spinning green is 3 times as great as the probability of spinning red. The probability of spinning red is twice as great as the probability of spinning blue. The number of yellow sections is equal to the number of blue sections. How many sections of each color are there? What is the probability of spinning each color?

Answer 1

reds --- x

greens -- 3x
blue ---- x/2
yellow --- x/2

x+3x+x/2+x/2 = 10
5x = 10
x = 2

2 reds
6 greens
1 blue
1 yellow

prob(red) = 2/10 = 1/5
etc

Answer 2

To answer this question, we need to set up an equation based on the given information.

Let's denote the number of green sections as G, the number of red sections as R, the number of yellow sections as Y, and the number of blue sections as B.

From the given information, we know that:
1) G + R + Y + B = 10 (since there are 10 equal sections on the spinner).
2) The probability of spinning green is 3 times as great as the probability of spinning red. So, the ratio of G to R is 3:1 or G = 3R.
3) The probability of spinning red is twice as great as the probability of spinning blue. So, the ratio of R to B is 2:1 or R = 2B.
4) The number of yellow sections is equal to the number of blue sections, so Y = B.

Now, let's substitute the value of G and R from equations 2 and 3 into the first equation:

3R + 2B + B + B = 10
3R + 4B = 10
Substituting R = 2B:
3(2B) + 4B = 10
6B + 4B = 10
10B = 10
B = 1

Substituting B = 1 into the equation R = 2B:
R = 2(1) = 2

Substituting B = 1 into the equation Y = B:
Y = 1

Substituting R = 2 and B = 1 into the equation G = 3R:
G = 3(2) = 6

So, there are 6 green sections, 2 red sections, 1 yellow section, and 1 blue section on the spinner.

To find the probability of spinning each color, divide the number of sections of that color by the total number of sections, which is 10.

Probability of spinning green: 6/10 = 3/5
Probability of spinning red: 2/10 = 1/5
Probability of spinning yellow: 1/10
Probability of spinning blue: 1/10

Therefore, the probability of spinning each color is 3/5 for green, 1/5 for red, 1/10 for yellow, and 1/10 for blue.