Subscribe

7th grade · Math · Unit 11 of 18

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.

Alabama Course of Study content standard: 7.16 · 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 Alabama

In the Alabama Course of Study, this is unit 11 of 18 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: Alabama State Department of Education (ALSDE)

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 2 blue marbles. You take out one marble, put it back, then take out another. What is the probability that both are red?

    • 10/21
    • 25/49
    • 5/7

  2. Question 2

    A bag has 2 red and 4 blue marbles. You take two marbles without putting the first one back. What is the probability that both are red?

    • 1/3
    • 1/9
    • 1/15

  3. Question 3

    A bag has 5 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?

    • 4/9
    • 1/2
    • 5/9

  4. Question 4

    A café has 4 kinds of sandwich and 6 kinds of drink. How many different sandwich-and-drink combinations are possible?

    • 24
    • 22
    • 14

  5. Question 5

    A bag has 2 red and 3 blue marbles. You take two marbles without putting the first one back. What is the probability that both are red?

    • 1/10
    • 4/25
    • 2/5

  6. Question 6

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

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

More 7th grade