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Cogito

Probability and Statistics · Chapter 4 · Lesson 2

Practice Worksheet

Conditional Probability

Given that something already happened.

12 problems · about 22 minutes · TEKS P.S.2.E, S-CP.B.6

NameDate

Figure — use these to answer the problems

Conditioning means using one bar as the new total instead of the sum of all of them.
Walk12
Bus8
Car5
Walk12
Bus8
Car5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. P(A and B) = 0.24, P(B) = 0.6. What is P(A given B)?

    Answer

  2. What does conditioning on B do?

    • It shrinks the sample space to just B.
    • It enlarges the sample space.

  3. P(A and B) = 0.3, P(B) = 0.6. P(A given B)?

    Answer

  4. P(A and B) = 0.1, P(B) = 0.4. P(A given B)?

    Answer

  5. 20 of 50 in a group have a trait. P(trait given the group)?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. P(A given B) = P(A) = 0.3. Are A and B independent? 1 yes, 0 no.

    Answer

  2. Is P(A given B) always equal to P(B given A)? 1 yes, 0 no.

    Answer

  3. A die shows an even number. What is P(it is a 6), 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. Put the conditional probability method in order.

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

    • Identify which event is the condition.
    • Use that event as the new total.
    • Count how many of those also satisfy the other event.
    • Divide to get the conditional probability.

  2. P(A and B) = 0.45, P(B) = 0.9. P(A given B)?

    Answer

  3. The Condition

    P(A and B) = 0.2 and P(B) = 0.5. What is P(A given B)?

    Answer

  4. The Table

    Of 60 sport players, 45 play music. What is P(music given sport)?

    Answer