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Cogito

Probability and Statistics · Chapter 3 · Lesson 2

Practice Worksheet

Sample Spaces and Simulation

List everything that could happen.

12 problems · about 21 minutes · TEKS P.S.2.B, S-IC.A.2

NameDate

Figure — use these to answer the problems

Four outcomes for two coins. Two of them contain exactly one head, which is why that result is twice as likely.
HH1
HT1
TH1
TT1
Head head1
Head tail1
Tail head1
Tail tail1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Three coins. How many outcomes in the sample space?

    Answer

  2. Why is P(exactly one head on two coins) not one third?

    • There are four outcomes, and two of them have one head.
    • Because coins are not fair.

  3. Three coins. How many outcomes?

    Answer

  4. Two coins. Probability of exactly one head, as a decimal?

    Answer

  5. Two dice. How many ways to total 7?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Two dice. Probability of a total of 7, as a decimal to three places?

    Answer

  2. A coin then a die. How many outcomes?

    Answer

  3. Which gives a steadier simulation estimate? 1 for 20 trials, 2 for 2000.

    Answer

Stretch Yourself

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

4 problems

  1. Put the steps of designing a simulation in order.

    Write 1 to 4 in the boxes to put these in order.

    • State what one trial represents.
    • Decide how the random device maps onto the situation.
    • Define what counts as a success.
    • Run many trials and divide successes by trials.

  2. Four coins. How many outcomes?

    Answer

  3. The Two Coins

    How many outcomes are in the sample space for two coins?

    Answer

  4. The Dice

    How many outcomes for two dice?

    Answer