Field Notesgrade 7 math
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Solution key: How likely

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Camp · How likely

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1 of 8 · chance-c01

A fair coin. P(heads), as a simplified fraction?

  1. A fair coin has two equally likely outcomes: heads and tails.
  2. One of those outcomes is heads.
  1. Probability = favorable outcomes / total outcomes = 1/2.
  2. Check: heads and tails each have chance 1/2; together they make 1.

Answer: 1/2

2 of 8 · chance-c02

A fair number cube, faces 1–6. P(rolling a 4), as a simplified fraction?

  1. A fair cube has six equally likely faces, 1 through 6.
  2. Only one face, 4, is the one we want.
  1. Probability = 1 favorable face / 6 total faces = 1/6.
  2. Check: each of the six faces has chance 1/6, and six of them add to 1.

Answer: 1/6

3 of 8 · chance-c03

A fair number cube. P(even), as a simplified fraction?

  1. Even faces are 2, 4, and 6.
  2. They are three of the six equally likely faces.
  1. Probability = 3/6; divide top and bottom by 3 to simplify to 1/2.
  2. Check: the other three faces are odd, so exactly half are even.

Answer: 1/2

4 of 8 · chance-c04

A fair spinner has 4 equal parts: red, blue, green, yellow. P(red), as a simplified fraction?

  1. The four equal spinner sections have equal chances.
  2. Only one section is red.
  1. Probability = 1 favorable section / 4 total sections = 1/4.
  2. Check: the three other colors total 3/4; 1/4 + 3/4 = 1.

Answer: 1/4

5 of 8 · chance-c05

A bag has 2 red and 3 blue marbles. You pick one at random. P(blue), as a simplified fraction?

  1. Count all marbles: 2 red + 3 blue = 5 total.
  2. We want blue; three marbles work. Each marble has the same chance in a random pick.
  1. Probability = 3 blue / 5 total = 3/5.
  2. Check: red is 2/5; 3/5 + 2/5 = 1.

Answer: 3/5

6 of 8 · chance-c06

P(rain) = 0.3. What is P(not rain), as a decimal?

  1. Rain and not rain cover all possibilities; their chances total 1.
  2. Rain uses 0.3 of that total. Not rain is what remains.
  1. 1 − 0.3 = 0.7. P(not rain) = 0.7.
  2. Check: 0.3 + 0.7 = 1, or 30% + 70% = 100%.

Answer: 0.7

7 of 8 · chance-c07

A fair number cube. P(greater than 4), as a simplified fraction?

  1. Greater than 4 means 5 and 6; 4 itself does not count.
  2. Two of six equally likely faces work.
  1. Probability = 2/6; divide top and bottom by 2 to get 1/3.
  2. Check: four faces fail, so 2/6 + 4/6 = 1.

Answer: 1/3

8 of 8 · chance-c08

A fair coin is flipped twice independently. P(two heads), as a simplified fraction?

  1. Each fair flip has heads or tails, and the independent flips do not change each other.
  2. Both-flip outcomes are HH, HT, TH, TT: four equally likely pairs.
  1. Only HH works, so probability = 1/4.
  2. Check another way: 1/2 × 1/2 = 1/4.

Answer: 1/4