Virginia SOL Math / Grade 8 / Probability & Statistics

8.PS.1

Independent & Dependent Events

What you'll learn

  • Determine whether two events are independent or dependent
  • Find the probability of two events occurring together
  • Apply the multiplication rule for probability

Words to know

Probability —
how likely an event is, from 0 to 1
Independent events —
events where one does not affect the other
Dependent events —
events where one affects the outcomes of the other
Sample space —
the set of all possible outcomes
Compound event —
an event made of two or more simple events

Why it matters Understanding independent and dependent events helps us reason about games, weather, and decisions where several things happen in a row.

Worked examples

Model ItI do

A coin is flipped and a die is rolled. Find P(heads and a 4).

These are independent. P(heads) is 1/2 and P(4) is 1/6. Multiply: (1/2)(1/6) = 1/12.

Try It TogetherWe do

A bag has 3 red and 2 blue marbles. Two are drawn without replacement. Find P(red then red).

These are dependent. First P(red) is 3/5. After removing a red, 2 red remain of 4, so P(red) is 2/4 = 1/2. Multiply: (3/5)(1/2) = 3/10.

Now YouYou do

A die is rolled twice. Find P(a 2, then an odd number).

Decide if the rolls are independent, then multiply the two probabilities. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Two coins are flipped. Find P(heads and heads).

  2. 2.A die is rolled twice. Find P(3 then 5).

  3. 3.Drawing two cards without replacing the first: independent or dependent events?

On Level

The core Quick Check from the book.

  1. 1.Two coins are flipped. Find P(heads and heads).

  2. 2.A die is rolled twice. Find P(6 then 6).

  3. 3.Are drawing cards without replacement independent or dependent events?

  4. 4.A bag has 4 red and 1 green. Two drawn with replacement. Find P(green then green).

  5. 5.A spinner has 4 equal parts. Spun twice. Find P(same part both times for a chosen part).

Challenge

Stretch your thinking.

  1. 1.A bag has 4 red and 6 blue marbles. Two are drawn without replacement. Find P(red then red).

  2. 2.A coin is flipped and a die is rolled. Find P(tails and an even number).

  3. 3.A bag has 2 green and 3 yellow. One is drawn, replaced, then another is drawn. Find P(green then yellow).