Graph the results of a coin toss:
Toss Coins
0 20
1 12
2 5
3 1
4 0
State an equation that best fits the results (use n to represent the number of the toss). What physical phenomenon does this model?
I was able to graph this, I just do not understand how to write the equation, or what it models???
To find an equation that best fits the results of the coin toss, you can use a regression model. A common type of regression model for this type of data is the exponential decay model.
In this case, you can observe that as the number of tosses increases (n increases), the number of coins decreases. This suggests an exponential decay relationship.
The general form of an exponential decay model is: y = a * (b)^x
In this equation:
- y represents the number of coins
- a is the initial value or the number of coins at the first toss
- b is the decay factor or the ratio of change from one toss to the next
- x is the number of tosses (n)
To find the specific values for a and b, you can use the data points you have:
For the first toss (n = 0), the number of coins is 20.
So, at n = 0, y = 20:
20 = a * (b)^0
20 = a
Now, we can use another data point to find the value of b. Let's use the second toss (n = 1), where the number of coins is 12.
So, at n = 1, y = 12:
12 = 20 * b^1
b = 12/20 = 0.6
Therefore, the equation that best fits the results of the coin toss is:
y = 20 * (0.6)^x
This equation represents a exponential decay model, where the number of coins decreases with each toss.
The physical phenomenon that this model represents is the concept of probability in a coin toss. As the number of tosses increases, the number of coins tends to decrease, which aligns with the expected outcome of a fair coin toss where roughly 50% probability exists for each outcome.