This worksheet is designed to help us investigate the distribution of flipping four coins.
1. List out every combination of Heads (H) and tails (T)
that you can get if you flip four coins.
1) 5) 9) 13)
2) 6) 10) 14)
3) 7) 11) 15)
4) 8) 12) 16)
(make sure you have 16 answers!!)
How many times did you get:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
2. By dividing these numbers by 16 (total #of possibilities),
we get the following probability chart.
X X=4H X=3H,1TX=2H,2TX=1H,3TX=4T
P(X) 0 0 0 0 0
3. Let's graph this table and see the "shape" of the
probabilities!!
1
9/10
4/5
7/10
3/5
1/2
Series1
2/5
3/10
1/5
1/10
0
X=4H X=3H,1T X=2H,2T X=1H,3T X=4T
4. So, how does this actually relate to actually flipping coins?
Well, we would expect that we would get all heads (or
all tails) 1/16 of the time, and so forth. But, is this true?
Let's find out!!
ACTIVITY
Take a penny, a nickel, a dime, and a quarter. Flip them
all one time and record below if they were heads or tails.
Penny Nickel Dime Quarter
FLIP 1
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
X X=4H X=3H,1TX=2H,2TX=1H,3TX=4T
P(X) 0 0 0 0 0
P(X)
1
4/5
3/5
P(X)
2/5
1/5
0
X=4H X=3H,1T X=2H,2T X=1H,3T X=4T
The graph of this result isn't anything like our original graph.
But, this is because our sample is too small.
So, let's flip again, and again, and again, and again
remembering to record our results after each flip.
Penny Nickel Dime Quarter
FLIP 2
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 3
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 4
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 5
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Now, we'll look at the occurance of all five flips:
X X=4H X=3H,1TX=2H,2TX=1H,3TX=4T
P(X) 0 0 0 0 0
P(X)
1
9/10
4/5
7/10
3/5
1/2
P(X)
2/5
3/10
1/5
1/10
0
X=4H X=3H,1T X=2H,2T X=1H,3T X=4T
What we should notice is that the shape of the graph is a little better
of a match then just doing 1 flip. So, let's do 15 more flips and see if
the shape becomes an even better match to our "theoretic" graph.
Penny Nickel Dime Quarter
FLIP 6
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 7
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 8
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 9
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 10
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 11
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 12
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 13
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 14
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 15
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 16
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 17
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 18
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 19
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Penny Nickel Dime Quarter
FLIP 20
For the combination above, put a 1 in the appropriate box:
4 Heads: 3 Heads: 2 Heads 1 Head: 0 Heads:
Let's look at the occurance of all 20 flips:
X X=4H X=3H,1TX=2H,2TX=1H,3TX=4T
P(X) 0 0 0 0 0
P(X)
1
9/10
4/5
7/10
3/5
1/2
P(X)
2/5
3/10
1/5
1/10
0
X=4H X=3H,1T X=2H,2T X=1H,3T X=4T
What do we notice now? How does this graph compare to the original
probability graph? What do you think would happen if you flipped the
coins 20 more times? 50 more times? 100 more times?
Write a summary of your observations of this activity.