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Cogito

Probability and Statistics · Chapter 4 · Lesson 1

Practice Worksheet

And, Or, and Independence

Combining two events.

12 problems · about 22 minutes · TEKS P.S.2.D, S-CP.A.2

NameDate

Figure — use these to answer the problems

Change the counts and consider drawing twice. Without replacement, the second draw faces different numbers.
Red4
Blue6
Red4
Blue6
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. P(A) = 0.5, P(B) = 0.2, independent. What is P(A and B)?

    Answer

  2. Why does the addition rule subtract P(A and B)?

    • The overlap would otherwise be counted twice.
    • To make the answer smaller.

  3. P(A) = 0.3, P(B) = 0.5, independent. P(A and B)?

    Answer

  4. P(A) = 0.2, P(B) = 0.3, mutually exclusive. P(A or B)?

    Answer

  5. Two dice. Probability both show six, as a decimal to three places?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. P(A) = 0.6, P(B) = 0.5, P(A and B) = 0.3. P(A or B)?

    Answer

  2. Are mutually exclusive events independent? 1 for yes, 0 for no.

    Answer

  3. Three fair coins. Probability all heads, as a decimal to three places?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each pair by whether the events are independent.

    Write each item under the heading it belongs to: Two separate coin tosses · Rolling a die twice · Two draws from a bag without replacement · Drawing an ace and drawing a king on one card

    Independent

    Not independent

  2. P(A) = 0.4, P(B) = 0.25, independent. P(A and B)?

    Answer

  3. The Two Coins

    Two fair coins. Probability both are heads, as a decimal?

    Answer

  4. The Overlap

    P(A) = 0.5, P(B) = 0.4, P(A and B) = 0.2. What is P(A or B)?

    Answer