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7th grade · Math · Unit 13 of 22

Dependent Events

With and without replacement

What your child practices

Telling independent from dependent events and finding the probability of two events, with and without putting the first item back.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 7.6(A); 7.6(D) · tree diagrams and the probability of compound events

How we explain it

Children can open this short lesson before they practice.

  1. Independent events do not change each other's chances.
  2. Dependent events do: drawing without putting back changes what is left.
  3. Multiply the chances of each step.

Example: A bag has 3 red and 2 blue marbles. You draw two red without putting any back. What is the probability? First red: 3/5. Second red, 2 left of 4: 2/4. 3/5 × 2/4 = 6/20 = 3/10. Answer: 3/10

Dependent Events in Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 13 of 22 in 7th grade Math, after Probability and before Samples & Populations.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Texas Education Agency (TEA)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A bag has 3 red and 3 blue marbles. You take two marbles without putting the first one back. What is the probability that both are red?

    • 1/4
    • 1/5
    • 1/2

  2. Question 2

    When two events are independent, the probability of both happening is found by…

    • adding their probabilities
    • subtracting their probabilities
    • multiplying their probabilities

  3. Question 3

    A bag has 3 red and 5 blue marbles. You take out a red marble and do not put it back. What is the probability that the second marble is red?

    • 3/7
    • 3/8
    • 2/7

  4. Question 4

    Which is true about picking two cards from a deck without putting the first back?

    • The probability of the second card depends on the first card.
    • The second pick is always certain.
    • The probabilities never change.

  5. Question 5

    You draw a card, put it back, then draw again. Are the two draws independent or dependent?

    • dependent
    • independent

  6. Question 6

    A bag has 5 red and 1 blue marbles. You take two marbles without putting the first one back. What is the probability that both are red?

    • 2/3
    • 5/6
    • 25/36

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