12.4. Building a Simulation¶

Let’s use what we have learned about random numbers and if statements to build a simulation. We want to know the answer to “If you flip a coin 100 times, what are the chances you get 5 heads in a row at some point?”

This is a complex problem. We need to flip a coin 100 times and figure out if we get at least 5 heads in a row - that is slightly different than what we have done so far. We will also need to repeat that a bunch of times - if we want to know the chances of something happening, we will need to do it say 10000 times and see what percent of the time we get the right result.

So let’s start with the basics - how do we see if we got 5 heads in a row? Well, each time we flip a coin, if it is a heads, we need to add one to headsInARow. If it is a tails, that means we now have seen 0 headsInARow:

Try running the program. Does it appear to work correctly? Once you have verified that the code appears to work, we need to modify it so it produces just one answer - true or false - yes we got at least 5 heads in a row or no we did not.

To do this, we will use break to stop the loop if we see 5 heads in a row. The break command is a way to stop a loop - it “breaks” us out of the loop and continues with the rest of the program. In this case, if headsInARow hits 5, we can stop the loop early - we know that we got 5 heads and we don’t want to keep going and flip a tails and then “forget” that we had 5 in a row.

I decide that I want to try to get 7 heads in a row. Which lines would I need to change in the program? (Use the history slider to go back to the original version if you made changes to it.)

4, 13, 16
We don't need to change the loop - we still want 100 flips.
13, 16
Correct.
7, 13, 16
We don't need to change how flips work. A 0 is still heads.
4, 7, 13, 16
We don't need to change the loop - we still want 100 flips.

Now, we want to turn the code into a function that returns True or False instead of printing the answer. Making it into a function will make it easier to repeat the process over and over.

Arrange the code so that the checkHeadsInRow(desiredStreak) function works correctly. It will take a number as its parameter - the number of heads in a row we want to see. It will do 100 flips and see if we get that many in a row. If so, it returns True, otherwise False. Using a parameter means we could use this same function to easily ask for 4 heads in a row, or 6 heads.

You will use all of the blocks. Make sure to put the import at the very top of the program and the main part of the program (the function call) after you define the function.

        def checkHeadsInRow(desiredStreak):
    headsInARow = 0 #start with 0
---
    for i in range(100):
---
        flip = random.randrange(0, 2)
---
        if flip == 0:
            headsInARow = headsInARow + 1
        else:
            headsInARow = 0
---
        if headsInARow == desiredStreak:
            break
---
    # Make final decision
    if headsInARow >= desiredStreak:
---
        return True
---
    else:
---
        return False

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12.4. Building a Simulation¶