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7th grade · Math · Unit 11 of 17

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.

Maine Learning Results learning standard: 7.SP.C.8 · probabilities of compound events with organized lists and tree diagrams

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 Maine

In the Maine Learning Results, this is unit 11 of 17 in 7th grade Math, after Algebra Moves and before Mean, Median & Mode.

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: Maine Department of Education

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

    • 16/81
    • 4/9
    • 1/6

  2. Question 2

    A bag has 3 red and 5 blue marbles. You take two marbles without putting the first one back. What is the probability that both are red?

    • 3/8
    • 3/28
    • 9/64

  3. Question 3

    A café has 5 kinds of sandwich and 2 kinds of drink. How many different sandwich-and-drink combinations are possible?

    • 10
    • 7
    • 20

  4. Question 4

    A bag has 5 red and 2 blue marbles. You take out a red marble and do not put it back. What is the probability that the second marble is red?

    • 2/3
    • 5/7
    • 5/6

  5. Question 5

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

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

  6. Question 6

    You take a marble from a bag and do not put it back. You take a second marble. Are the two picks independent or dependent?

    • dependent
    • independent

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