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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.

California Content Standards learning standard: 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

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 café has 3 kinds of sandwich and 3 kinds of drink. How many different sandwich-and-drink combinations are possible?

    • 15
    • 9
    • 14

  2. Question 2

    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
    • 1/2
    • 1/4

  3. Question 3

    A bag has 3 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?

    • 3/8
    • 9/64
    • 3/28

  4. Question 4

    A bag has 5 red and 1 blue marbles. You take out a red marble and do not put it back. What is the probability that the second marble is red?

    • 4/5
    • 1
    • 5/6

  5. Question 5

    A bag has 2 red and 1 blue marbles. You take two marbles without putting the first one back. What is the probability that both are red?

    • 1/3
    • 4/9
    • 2/3

  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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