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Cogito

Probability and Statistics · Chapter 5 · Lesson 3

Practice Worksheet

Binomial Situations

Counting successes in a fixed number of tries.

12 problems · about 22 minutes · TEKS P.S.2.G, S-MD.A.3

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, p = 0.5. What is the mean number of successes?

    Answer

  2. Why is drawing cards without replacement not binomial?

    • The trials are not independent, since the deck changes.
    • There are too many cards.

  3. n = 20, p = 0.5. Mean number of successes?

    Answer

  4. n = 50, p = 0.2. Mean?

    Answer

  5. 5 tosses. How many patterns have exactly 2 heads?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 4 tosses of a fair coin. P(exactly 2 heads), as a decimal to three places?

    Answer

  2. How many conditions must a binomial setting satisfy?

    Answer

  3. n = 100, p = 0.3. Mean?

    Answer

Stretch Yourself

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

4 problems

  1. Which settings are binomial?

    • Tossing a coin 10 times and counting heads
    • Asking 50 people a yes-or-no question
    • Tossing until the first head appears
    • Drawing 5 cards without replacement
    • Tick every box that applies.

  2. n = 12, p = 0.25. Mean?

    Answer

  3. The Mean

    40 tosses of a fair coin. What is the mean number of heads?

    Answer

  4. The Patterns

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

    Answer