Question

duke has a spinner that is divided into six equal - sized sections. each section is a different color. he spun the spinner multiple times, and his results are shown below.
spinner results

color	number of spins

| red |
| blue |
| green |
| yellow |
| purple |
| brown |
based on the data, what is the experimental probability that the next time duke spins the spinner, it will land on red?
a.

b.

c.

d.

Explanation:

Step1: Count spins for red

Red has \(5 + 3 = 8\)? Wait, no, tally marks: first group is 5 (|||||), then 3? Wait, no, the first red tally is \(\cancel{|||||}\) (which is 5 with a cross, so 5) and then ||| (3), so total \(5 + 3 = 8\)? Wait, no, wait blue: two groups of 5 (each \(\cancel{|||||}\)) and then ||, so \(5 + 5 + 2 = 12\). Green: |||| (4). Yellow: \(\cancel{|||||}\) (5) and ||| (3), so \(5 + 3 = 8\). Purple: |||| (4). Brown: |||| (4). Wait, let's recalculate:

Red: \(\cancel{|||||}\) (5) + ||| (3) = 8? Wait, no, \(\cancel{|||||}\) is 5, then ||| is 3, so 5 + 3 = 8.

Blue: \(\cancel{|||||}\) (5) + \(\cancel{|||||}\) (5) + || (2) = 5 + 5 + 2 = 12.

Green: |||| (4).

Yellow: \(\cancel{|||||}\) (5) + ||| (3) = 8.

Purple: |||| (4).

Brown: |||| (4).

Now total spins: 8 (red) + 12 (blue) + 4 (green) + 8 (yellow) + 4 (purple) + 4 (brown) = 8 + 12 = 20; 20 + 4 = 24; 24 + 8 = 32; 32 + 4 = 36; 36 + 4 = 40. Wait, total spins are 40? Wait, red: 8? Wait, no, maybe I miscounted red. Wait the red tally: \(\cancel{|||||}\) is 5, then ||| is 3? Wait, no, \(\cancel{|||||}\) is 5 (the cross is to make 5), then ||| is 3, so 5 + 3 = 8. Blue: two \(\cancel{|||||}\) (5 each) and || (2), so 5*2 + 2 = 12. Green: 4, yellow: 5 + 3 = 8, purple: 4, brown: 4. So total: 8 + 12 + 4 + 8 + 4 + 4 = 40.

Step2: Experimental probability formula

Experimental probability of red is \(\frac{\text{number of red spins}}{\text{total spins}}\). Red spins: let's check again. Wait, maybe I messed up red's tally. Wait the red tally is \(\cancel{|||||}\) (5) and then ||| (3)? Wait, no, \(\cancel{|||||}\) is 5, then ||| is 3, so 5 + 3 = 8? Wait, but let's count again:

Wait, the first red tally: \(\cancel{|||||}\) (which is 5) and then ||| (3), so 5 + 3 = 8. Blue: two \(\cancel{|||||}\) (5 each) and || (2), so 5*2 + 2 = 12. Green: |||| (4). Yellow: \(\cancel{|||||}\) (5) and ||| (3), so 5 + 3 = 8. Purple: |||| (4). Brown: |||| (4). So total spins: 8 + 12 + 4 + 8 + 4 + 4 = 40. So red spins: 8? Wait, no, wait the problem's options: D is 7/40. Wait, maybe I miscounted red. Let's look at the tally again. Red: \(\cancel{|||||}\) (5) and then |||? Wait, no, maybe the first group is 5 (with cross) and then 3? Wait, no, maybe the red tally is \(\cancel{|||||}\) (5) and then ||| (3)? Wait, but 5 + 3 = 8. But 8/40 = 1/5, but option A is 1/5? Wait no, option A is 1/5? Wait the options: A is 1/5, B is 1/6, C is 3/10, D is 7/40. Wait, maybe I made a mistake in red's count. Let's re-express the tally marks:

- Red: \(\cancel{|||||}\) (which is 5) and then ||| (3)? Wait, no, \(\cancel{|||||}\) is 5, then ||| is 3, so 5 + 3 = 8.

- Blue: \(\cancel{|||||}\) (5) + \(\cancel{|||||}\) (5) + || (2) = 12.

- Green: |||| (4).

- Yellow: \(\cancel{|||||}\) (5) + ||| (3) = 8.

- Purple: |||| (4).

- Brown: |||| (4).

Total: 8 + 12 + 4 + 8 + 4 + 4 = 40. So red is 8? 8/40 = 1/5, which is option A. But wait, maybe the red tally is 7? Wait, maybe the first group is 5 (with cross) and then 2? Wait, no, the red tally is \(\cancel{|||||}\) (5) and then ||| (3), so 5 + 3 = 8. Wait, 8/40 = 1/5, which is option A. But let's check again. Wait, maybe the red tally is 7. Let's see: \(\cancel{|||||}\) is 5, then || (2)? No, the image shows red as \(\cancel{|||||}\) and then |||. So 5 + 3 = 8. 8/40 = 1/5, which is option A. But wait, the options: A is 1/5, B is 1/6, C is 3/10, D is 7/40. So maybe I made a mistake. Wait, let's count total spins again:

Red: 8, Blue: 12, Green: 4, Yellow: 8, Purple: 4, Brown: 4. 8+12=20, +4=24, +8=32, +4=36, +4=40. Correct. So red is 8, 8/40=1/5. So option A.

Wait, but maybe the red tally is 7. Let's check the image again. The red tally: first group is \(\cancel{|||||}\) (5) and then |||? Wait, no, maybe the first group is 5 (with cross) and then 2? Wait, the user's image: red has \(\cancel{|||||}\) (5) and then ||| (3), so 5+3=8. So 8/40=1/5, which is option A.

Answer:

A. \(\frac{1}{5}\)