on a game board, landing on blue means to move ahead 1 space , landing on red means to move ahead 2 spaces, and landing on orange means to move back 1 space. if you took 30 spins about where would you expect to be on the game board, relative to where you started?
i would be about ----- spaces-------.
(ahead or
behind)
You have a 1/3 probability of landing on each color. So, you probably will land on blue 10 times, red 10 times, and orange 10 times. With all those blues, you will have gone forward 10 spaces. With all those oranges, you would have gone back 10 spaces. You are still at your starting point. But, with 10 reds, you would move up 20 spaces. So, theoretically, you would be about 20 spaces ahead.
red
How to do math?
Hey if you're in mrs Crose's class you probably know who I am if you read my name
Wow, it sounds like you've been on quite the colorful adventure! With all those spins, you'd most likely find yourself about 20 spaces ahead of where you started. So not only are you winning the game, but you're also winning at life! Keep up the good spins, my friend!
To calculate the expected position on the game board, we need to determine the net movement for each color and then sum them up.
Given that landing on blue moves you ahead 1 space, landing on red moves you ahead 2 spaces, and landing on orange moves you back 1 space, we can determine the net movement for each color:
- Blue: Moves ahead 1 space (probability = 1/3)
- Red: Moves ahead 2 spaces (probability = 1/3)
- Orange: Moves back 1 space (probability = 1/3)
Now, let's calculate the net movement for each color by multiplying the probability of landing on that color by the corresponding movement:
- Net movement for blue = (1/3) * 1 = 1/3
- Net movement for red = (1/3) * 2 = 2/3
- Net movement for orange = (1/3) * (-1) = -1/3
Next, we need to calculate the total net movement by summing up the net movements for each color:
Total net movement = Net movement for blue + Net movement for red + Net movement for orange
= 1/3 + 2/3 + (-1/3)
= 2/3
Since the total net movement is positive (2/3), it means that, on average, you are expected to be ahead on the game board relative to where you started. To be more specific, since each spin represents 1 move, after 30 spins, you would expect to be about (30 * 2/3) = 20 spaces ahead.