# Coin Toss Probability

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In this activity, you will explore some ideas of probability by using Excel to simulate tossing a coin and throwing a free throw in basketball. Toss a coin 10 times and after each toss, record in the following table the

result of the toss and the proportion of heads so far. For example, suppose you obtain the following sequence of heads and tails for the first five tosses: H T T T H. After the first toss, the proportion of heads so far is one out of one: _ 11_ or 1. After the second toss, the proportion of heads so far is one out of two: _12_ . After the third toss, the proportion of heads is one out of three: _ 13_ . After the fourth toss, the proportion of heads is one out of four: _14_ . After the fifth toss, the proportion of heads is two out of five: _ 25_ .

Toss # 1 2 3 4 5 6 7 8 9 10

H or T?

Prop of H So Far

1.

SSAc18.

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The solution examines the coin toss probability.

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In this activity, you will explore some ideas of probability by using Excel to simulate tossing a coin and throwing a free throw in basketball. Toss a coin 10 times and after each toss, record in the following table the result of the toss and the proportion of heads so far. For example, suppose you obtain the following sequence of heads and tails for the first five tosses: H T T T H. After the first toss, the proportion of heads so far is one out of one: 1/1 or 1. After the second toss, the proportion of heads so far is one out of two: 1/2. After the third toss, the proportion of heads is one out of three: 1/3. After the fourth toss, the proportion of heads is one out of four: 1/4. After the fifth toss, the proportion of heads is two out of five: 2/5.

Toss # 1 2 3 4 5 6 7 8 9 10

H or T? T H H T T T T H H H

Prop of H so far 0.00 0.50 0.67 0.50 0.40 0.33 0.29 0.38 0.44 0.50

The above graph shows us that the proportion of heads at the beginning of the trials is more variable than at the end. As the number of flips increases, it seems that that proportion of heads so far approaches ½. This seems to be born out in the above chart.

Activity 18.1, question 3, p. 577-578 (Sevilla, A., & Somers, K., 2007).

Now, you will use Excel to simulate 1000 independent tosses of a fair coin and plot on a graph the proportion of heads so far after each toss using the instructions that follow in the table "Instructions to Use Excel to Simulate Tossing a Coin."

In Excel, the function RAND() (that is, RAND followed by two parentheses) produces a decimal number between 0 and 1, in such a way that every decimal number between 0 and 1 is equally likely to be produced. You will use the RAND() function to generate integers 0 or 1 with equal probability. The integer 1 will signify "heads" and the integer 0 will signify "tails." To get a 0 or 1 with equal probability, you'll multiply the random number by 2 and then take the integer part of it; that is, you will drop all digits after the decimal point. Suppose the decimal number produced is 0.13061. What value do you get if you multiply that number by 2 and then take the integer part of it?

You would get a 0.

Suppose the decimal number produced is 0.78934. What value do you get if you multiply that number by 2 and then take the integer part of ...

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