Branch each first choice into every second choice. Multiply to count: 3 suits × 3 badges = 9. Probability is matching outcomes over all outcomes: 1/9.
outcomeone possible result
tree diagrambranches that show every outcome
probabilitymatching outcomes out of all outcomes
Watch for: Adding the choices (3 + 3) instead of multiplying them (3 × 3). Leaving out an outcome by missing a branch or a table cell.
At home: Lay out 2 shirts and 3 pairs of pants and list every outfit together. Check the count with 2 × 3 = 6.
Sample sheet and answer key
Luna's Space Adventure
Grade 5 · Outcomes and probability · 5.PS.3
NameDate
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Tree diagram
Orion picks a badge and a suit, any one equally likely. Write every outcome.
How many outcomes?
Probability of comet and red?
Probability the suit is red?
Every outcome
Toss a coin (H or T) and roll a number cube. Write every outcome, like H1.
1
2
3
4
5
6
H
T
How many outcomes?
Probability of H and an even number?
Probability of a 1 or a 2?
Multiply to count
Choices for each pick, multiplied, give every way.
1
Nova picks a suit (red, silver or blue) and a helmet (pointy or square). How many different ways can Nova choose?
ways
2
Orion picks a badge (planet, moon, star or comet), a helmet (square, pointy or round) and a suit (blue, white, red or silver). How many different ways can Orion choose?
ways
Sheet
Luna's Space Adventure
Grade 5 · Outcomes and probability · 5.PS.3
Answer key
Astronaut Luna is exploring a far-off corner of space. Solve each problem to help Luna's mission go smoothly!
Tree diagram
Orion picks a badge and a suit, any one equally likely. Write every outcome.
How many outcomes?6
Probability of comet and red?1/6
Probability the suit is red?2/6 = 1/3
Every outcome
Toss a coin (H or T) and roll a number cube. Write every outcome, like H1.
1
2
3
4
5
6
H
H1
H2
H3
H4
H5
H6
T
T1
T2
T3
T4
T5
T6
How many outcomes?12
Probability of H and an even number?3/12 = 1/4
Probability of a 1 or a 2?4/12 = 1/3
Multiply to count
Choices for each pick, multiplied, give every way.
1
Nova picks a suit (red, silver or blue) and a helmet (pointy or square). How many different ways can Nova choose?
3 × 2 = 6
6ways
2
Orion picks a badge (planet, moon, star or comet), a helmet (square, pointy or round) and a suit (blue, white, red or silver). How many different ways can Orion choose?
4 × 3 × 4 = 48
48ways
Answer key
New problems every time, three levels (gentle, core and stretch), themes to pick from, a second page if you want one. Each sheet comes with an answer key and a one-page guide for grown-ups.
