7th grade · Math · Unit 7 of 17
Probability
Chances of two events
What your child practices
Listing outcomes of two independent events (like a coin and a die), finding theoretical probabilities by multiplying, and comparing them with experimental results.
Alaska content standards learning standard: 7.SP.5; 7.SP.7; 7.SP.8 · probability of chance events and compound events
How we explain it
Children can open this short lesson before they practice.
- Probability = favorable outcomes ÷ all possible outcomes.
- It is always between 0 (impossible) and 1 (certain).
- For two events, list every outcome so none are missed.
Example: You roll a die. What is the probability of an even number? Even numbers: 2, 4, 6. That is 3 outcomes. There are 6 outcomes in all. 3/6 = 1/2. Answer: 1/2
Probability in Alaska
In the Alaska content standards, this is unit 7 of 17 in 7th grade Math, after Volume and before Fractions.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Alaska Department of Education and Early Development
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Two coins were flipped together 40 times. Based on these results, what is the experimental probability of "one head, one tail"? Give a fraction.
40 flips of two coins Result Count Two heads 9 One head, one tail 17 Two tails 14 answer box
17/40
Hint: Experimental probability = times it happened ÷ total trials = 17/40.
Question 2
Two spinners are each half red and half blue. Kenji spun both 200 times, and both landed on red 60 times. What is the experimental probability of "both red" as a percent?
answer box%
30 %
Hint: Experimental probability = 60/200 = 0.3 = 30%. Compare it with the theoretical probability: 1/2 × 1/2 = 1/4 = 25%.
Question 3
You flip a coin and roll a standard die (1 to 6). What is the probability of getting tails and a number greater than 4? Give a fraction.
answer box
1/6
Hint: The events are independent, so multiply: P(tails) × P(a number greater than 4) = 1/2 × 2/6 = 2/12 = 1/6.
Question 4
You roll a standard die (1 to 6) and spin a spinner with 5 equal sections. How many different outcomes are possible?
answer box
30
Hint: Each of the 6 results of the first event can pair with each of the 5 results of the second: 6 × 5 = 30 outcomes. A tree diagram or table shows them all.
Question 5
Which pair of events is independent?
- Flipping a coin, then rolling a die
- Taking a marble from a bag, then taking another without putting the first back
- Picking a team captain, then picking a co-captain from the students left
- Drawing a card, then drawing a second card without replacing the first
Flipping a coin, then rolling a die
Hint: When the first item isn't put back, the second pick has different chances, so those events depend on each other.
Question 6
The table shows every outcome of flipping a coin (H or T) and rolling a die. How many outcomes show a 5 or a 6 (with either coin side)?
Coin 1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6 answer box
4
Hint: Find the matching cells: H5, H6, T5, T6. That's 4 of the 12 outcomes.