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7th grade · Math · Unit 10 of 20

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.

New York State Learning Standards learning standard: NY-7.SP.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 New York

In the New York State Learning Standards, this is unit 10 of 20 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: New York State Education Department (NYSED)

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

    • 2/9
    • 1/4
    • 1/2

  2. Question 2

    You spin a spinner twice. Are the two spins independent or dependent?

    • independent
    • dependent

  3. Question 3

    A bag has 4 red and 5 blue marbles. You take out one marble, put it back, then take out another. What is the probability that both are red?

    • 1/6
    • 4/9
    • 16/81

  4. Question 4

    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

  5. Question 5

    A bag has 3 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?

    • 3/4
    • 1/2
    • 3/5

  6. Question 6

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

    • independent
    • dependent

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