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Data Session 8, Part C: Analyzing Binomial Probabilities
 
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Session 8, Part C:
Analyzing Binomial Probabilities

In This Part: Making a Tree Diagram | Probability Tables | Binomial Experiments
Pascal's Triangle

Our coin tosses have been an example of a binomial experiment. A binomial experiment consists of n trials, where each trial is like a coin toss with exactly two possible outcomes. In each trial, the probability for each outcome remains constant.

In the previous section, we used a tree diagram to help us determine one particular outcome of a binomial experiment of n = 4 trials: the number of heads resulting from four tosses of a fair coin. These outcomes can be represented by the table you created in Problem C4:

Number of Heads

Frequency

Probability

0

1

1/16

1

4

4/16

2

6

6/16

3

4

4/16

4

1

1/16

Let's take a look at the patterns that emerge when you run this binomial experiment several times, each time increasing the number of trials:

One Toss

Number of Heads

Frequency

0

1

1

1

Two Tosses

Number of Heads

Frequency

0

1

1

2

2

1

Three Tosses

Number of Heads

Frequency

0

1

1

3

2

3

3

1

Four Tosses

Number of Heads

Frequency

0

1

1

4

2

6

3

4

4

1

If you display these possible outcomes in the following format, you'll find that they form what's known as Pascal's Triangle:


Next > Part C (Continued): Pascal's Triangle

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