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Find Probabilities of Compound Events as Fractions of Outcomes

Students understand that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. They use organized lists, tables, and tree diagrams to represent sample spaces and compute compound event probabilities.

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Find Probabilities of Compound Events as Fractions of Outcomes

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

5 of 8 equally likely outcomes: P(not) =

How it is taught

0:00 of 3:55

A compound probability is a fraction of the sample space.

List the outcomes, then count the ones that match.

Read it: Sample spaces as grids

Roll two dice and every outcome is one cell of a 6 by 6 grid: 6 × 6 = 36 outcomes. A sum of 7 holds 6 of them, 1,6 2,5 3,4 4,3 5,2 and 6,1, so P = 6/36 = 1/6.

  1. Draw the grid: one die's faces down the side, the other's across the top.
  2. Count every cell: the rows times the columns.
  3. Count the event's cells; P is that count over all of them.

Every face of one die meets every face of the other, so the grid holds 6 × 6 cells.

3,4 and 4,3 are different outcomes: the first die shows 3 in one and 4 in the other.

Every cell is equally likely, so P is the event's cells over all 36: 6/36 = 1/6.

The sample space is the rows times the columns; an event is the cells that fit it.

Counting 3,4 and 4,3 as one outcome: 3 cells instead of 6.

They are two cells of the grid, so a sum of 7 holds 6 outcomes.

16 of 36 equally likely outcomes: P = ___ — 4/9. 16 of the 36 outcomes: 16/36 = 4/9.

P(two heads when tossing a coin twice)

Let's toss a coin two times in a row. What's the probability we get two heads?

To find a probability, we need every possible outcome. We'll use a tree diagram to list them.

On the first toss, the coin lands either Heads or Tails.

On the second toss, each of those branches can ALSO land Heads or Tails.

Following each path gives us four outcomes: H-H, H-T, T-H, and T-T.

So the sample space has four equally likely outcomes.

Now let's find the outcomes that match our event — two heads.

Only one outcome works: H-H.

Probability is the number of favorable outcomes over the total number of outcomes.

That's one over four.

The probability of getting two heads is one-fourth — twenty-five percent. Nicely done!

Toss a coin twice — P(two heads)?Sample space for tossing a coin twiceStartHTHTHTOutcomesH HH TT HT T4 total1 favorableP(2 heads) =favorable / total14PROBABILITY14= 25%
Grade 7 · Sample spaces and compound events

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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