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7th grade Two-step chance: lists, tables and trees worksheet

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Two-step chance: lists, tables and trees

Grade 7 Math Worksheet

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Circle the best answer, or write your answer on the line.

  1. Esme rolls a fair number cube and flips a fair coin. What is the chance of a number 4 or greater and heads, in simplest form?

  2. Luz flips a fair coin and spins a spinner with 4 equal parts numbered 1 to 4. What is the chance of heads and a 4, as a percent?

  3. Milo flips two fair coins. What is the chance of two heads, as a percent?

  4. Noah draws one of 5 cards numbered 1 to 5 without looking and flips a fair coin. What is the chance of a card showing 1 or 5, and heads, as a percent?

  5. Tala rolls two fair number cubes. What is the chance that the sum is 9, in simplest form?

  6. Bo flips two fair coins. What is the chance of at least one head, in simplest form?

  7. Esme spins two spinners, each with 4 equal parts: red, blue, green, yellow. What is the chance that the two colors are different, in simplest form?

  8. Kira spins two spinners, each with 3 equal parts: red (R), blue (B), green (G). Which is the whole list of outcomes for both spinners?

    • RR, RB, RG, BR, BB, BG, GR, GB, GG
    • R, B, G
    • RR, RB, RG, BB, BG, GG
    • RR, RB, RG, BR, BB, BG, GR, GB

  9. Read this first

    Tree

    The spinner splits into 1, 2 and 3; each of those splits into H and T. Leaves: 1-H, 1-T, 2-H, 2-T, 3-H, 3-T.

  10. Noah spins a spinner with 3 equal parts numbered 1 to 3, then flips a fair coin, as the tree shows. What is the chance of an odd number and tails, in simplest form?

  11. Tree

    The card splits into red and blue; each of those splits into 1, 2, 3 and 4. Leaves: red-1, red-2, red-3, red-4, blue-1, blue-2, blue-3, blue-4.

  12. Pia picks 1 of 2 cards (1 red, 1 blue) without looking, then spins a spinner (1 to 4, equal parts). What is the chance of blue and a number over 2, in simplest form?

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7th grade Two-step chance: lists, tables and trees worksheet – printable
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About this worksheet

Two-step chance: lists, tables and trees. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can list every outcome of two steps (a coin then a spinner, two spinners, two number cubes) as a list, a table or a tree.
  • I can find the chance of a two-step event as the cells that count ÷ all the cells, even when it is described in words like "at least one head".
  • I can see that a sum or two orders (HT and TH) are not equally likely outcomes, and that taking an item out changes the second step.

Standard: 7.SP.C.8a, 7.SP.C.8b

Words to know

compound event: An event made of two or more steps, like a coin flip and then a spin.

sample space: The list of every possible outcome of all the steps. A table or tree shows it.

table (outcome table): Rows for the first step, columns for the second. Each cell is one outcome.

tree diagram: Branches for the first step, each splitting into the second step. Each leaf is one outcome.

at least one: One or more. It includes having two or three.

without putting back: The first item stays out, so the second step has one fewer choice.

Common mistakes

Your child added the numbers of outcomes of the steps instead of multiplying them.

Your child counted the outcomes of one step only.

Your child compared the outcomes that count with the ones that don't instead of with all of them.

What to say

Ask: how many pairs does each first outcome make?

Ask: what does the list need for both steps together?

Ask: out of how many outcomes in all?

Questions parents ask

What is the most common mistake with two-step chance: lists, tables and trees?

Your child added the numbers of outcomes of the steps instead of multiplying them.

How can I help my child with two-step chance: lists, tables and trees?

Ask: how many pairs does each first outcome make?

Are these 7th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 7 math

See all grade 7 math

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