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Cogito

AP Statistics · Chapter 2 · Lesson 3

Practice Worksheet

Binomial and Geometric Distributions

Counting successes, and waiting for the first.

12 problems · about 22 minutes · UNC-3.A, UNC-3.B

NameDate

Figure — use these to answer the problems

Four coin tosses. The middle counts have more patterns, which is why the distribution peaks there.
0 heads1
1 head4
2 heads6
3 heads4
Patterns with 0 heads1
Patterns with 1 head4
Patterns with 2 heads6
Patterns with 3 heads4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. n = 60 and p = 0.5. What is the mean number of successes?

    Answer

  2. What separates a geometric setting from a binomial one?

    • The number of trials is not fixed; you wait for the first success.
    • The probability changes between trials.

  3. n = 100, p = 0.3. Mean number of successes?

    Answer

  4. n = 100, p = 0.5. Standard deviation?

    Answer

  5. Geometric with p = 0.25. Expected trials until the first success?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. How many conditions must a binomial setting satisfy?

    Answer

  2. 4 fair coin tosses. How many patterns have exactly 2 heads?

    Answer

  3. 4 fair coin tosses. P(exactly 2 heads), to three decimal places?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each setting by its distribution.

    Write each item under the heading it belongs to: Successes in 20 fixed trials · Heads in 10 coin tosses · Tosses until the first head · Attempts until the first success

    Binomial

    Geometric

  2. n = 50, p = 0.2. Mean number of successes?

    Answer

  3. The Mean

    n = 40 and p = 0.5. What is the mean number of successes?

    Answer

  4. The Wait

    A geometric setting with p = 0.2. What is the expected number of trials until the first success?

    Answer