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📊 7th grade math · Data & Chance

Two things at once

List every outcome of both steps. Two flips: HH, HT, TH, TT. P(two heads) = 1/4. A coin and a 6-sided die have 12 outcomes. P(heads and a 5) = 1/12.

Worked example

A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting heads and a number greater than 3? (Any fraction with the right value counts, so you do not have to reduce it.)
Answer: 1/4
The sample space has 2 × 6 = 12 equally likely outcomes. The outcomes that fit are (H, 4), (H, 5), (H, 6): that is 3. So the probability is 312 = 14. Or multiply the two steps: 12 × 36 = 14. Answer: 1/4.

For grown-ups: Compound events: lists, tables, tree diagrams, simulation. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 7.SP.C.8
What this practises, for teachers

Practices compound events: lists, tables, tree diagrams, simulation (7.SP.C.8). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. A fair coin is flipped twice. What is the probability of getting two heads? (Any fraction with the right value counts, so you do not have to reduce it.)
    Show the answer and how
    Answer: 1/4
    The sample space has 2 × 2 = 4 equally likely outcomes. The outcomes that fit are (H, H): that is 1. So the probability is 14. Or multiply the two steps: 12 × 12 = 14. Answer: 1/4.
  2. A fair coin is flipped twice. What is the probability of getting at least one head? (Any fraction with the right value counts, so you do not have to reduce it.)
    Show the answer and how
    Answer: 3/4
    The sample space has 2 × 2 = 4 equally likely outcomes. The outcomes that fit are (H, H), (H, T), (T, H): that is 3. So the probability is 34. Answer: 3/4.
  3. A bag has 1 black and 5 white marbles. A marble is picked at random and put back, then a second marble is picked at random. What is the probability of getting two black marbles? (Any fraction with the right value counts, so you do not have to reduce it.)
    Show the answer and how
    Answer: 1/36
    The sample space has 6 × 6 = 36 equally likely outcomes. The outcomes that fit are (black, black): that is 1. So the probability is 136. Or multiply the two steps: 16 × 16 = 136. Answer: 1/36.

Before and after

Learn first: Fair and unfair chances (7th)

Name: ____________________Date: ____________Score: ____ / 12

Two things at once (7th grade)

  1. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting heads and a number greater than 2? (Any fraction with the right value counts, so you do not have to reduce it.)
  2. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting tails and an even number? (Any fraction with the right value counts, so you do not have to reduce it.)
  3. A fair coin is flipped twice. What is the probability of getting heads on the first flip and tails on the second flip? (Any fraction with the right value counts, so you do not have to reduce it.)
  4. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting heads and a number greater than 4? (Any fraction with the right value counts, so you do not have to reduce it.)
  5. A fair coin is flipped twice. What is the probability of getting heads on the first flip and tails on the second flip? (Any fraction with the right value counts, so you do not have to reduce it.)
  6. A fair coin is flipped twice. What is the probability of getting at least one head? (Any fraction with the right value counts, so you do not have to reduce it.)
  7. A fair coin is flipped and a fair six-sided die is rolled. What is the probability of getting heads and a number greater than 3? (Any fraction with the right value counts, so you do not have to reduce it.)
  8. A fair coin is flipped twice. What is the probability of getting two heads? (Any fraction with the right value counts, so you do not have to reduce it.)
  9. A fair coin is flipped twice. What is the probability of getting two tails? (Any fraction with the right value counts, so you do not have to reduce it.)
  10. A fair coin is flipped twice. What is the probability of getting exactly one head? (Any fraction with the right value counts, so you do not have to reduce it.)
  11. A bag has 6 yellow and 1 blue marbles. A marble is picked at random and put back, then a second marble is picked at random. What is the probability of getting two yellow marbles? (Any fraction with the right value counts, so you do not have to reduce it.)
  12. Spinner A has 4 equal sections: black, orange, blue and green. Spinner B has 6 equal sections numbered 1 to 6. Both spinners are spun. What is the probability of getting green or orange on the first spinner and 5 or more on the second? (Any fraction with the right value counts, so you do not have to reduce it.)

Answer key

  1. 1/3
  2. 1/4
  3. 1/4
  4. 1/6
  5. 1/4
  6. 3/4
  7. 1/4
  8. 1/4
  9. 1/4
  10. 1/2
  11. 36/49
  12. 1/6

More 7th grade skills: all 7th grade math skills, or every grade at math skills.