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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

If we assume that the coin is fair, each outcome (heads or tails) of a single toss is equally likely. This probability table summarizes the mathematical probability for the number of heads resulting from one toss of a fair coin:

Face

Frequency

Probability

1

1

1/2

0

1

1/2

Let's take a closer look at the tree diagram for two coin tosses. Each red branch represents the result heads (or H). Each blue branch represents the result tails (or T). The outcome associated with each path is indicated at the end of the path, together with the number of heads in that outcome.

Since we are tossing a fair coin, each of the four outcomes (HH, HT, TH, TT) is equally likely. Note 8

Problem C1

Solution  

Use this tree diagram to explain why the likelihood of getting exactly one head in two coin tosses is not the same as the likelihood of getting zero heads in two coin tosses.

What is the probability of each possible outcome? The possible values for the number of heads from two tosses are two (HH), one (HT, TH), or zero (TT).

This probability table summarizes the mathematical probabilities for the number of heads resulting from two tosses of a fair coin:

Number of Heads

Frequency

Probability

0

1

1/4

1

2

2/4

2

1

1/4


 

Problem C2

Solution  

On a piece of paper, draw a tree diagram for three tosses of a fair coin. Label and tally all the possible outcomes as in the previous examples.


 

Problem C3

  

Complete the probability table for three tosses of a fair coin:

Number of Heads

Frequency

Probability

0

1

1

2

3

show answers

 

Number of Heads

Frequency

Probability

0

1

1/8

1

3

3/8

2

3

3/8

3

1

1/8

hide answers


 
 

When you toss a fair coin four times, there are 16 possible outcomes (2 x 2 x 2 x 2), and each is equally likely. Here is the tree diagram for four tosses:


 

Problem C4

  

Complete the probability table for four tosses of a fair coin:

Number of Heads

Frequency

Probability

0

1

1

2

3

4

show answers

 

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

hide answers


 

Problem C5

Solution  

Do you think a tree diagram would help you create a similar probability table for 10 tosses of a fair coin? Why or why not?


 
 

Problem C5 suggests that we may need to find a pattern to the probability tables in this section in order to use them for problems involving larger numbers.


Next > Part C (Continued): Binomial Experiments

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