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.
Maine Learning Results learning standard: 7.SP.C.5; 7.SP.C.7; 7.SP.C.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 Maine
In the Maine Learning Results, 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: Maine Department of Education
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
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 2
You flip a coin and roll a standard die (1 to 6). What is the probability of getting tails and a 1? Give a fraction.
answer box
1/12
Hint: The events are independent, so multiply: P(tails) × P(a 1) = 1/2 × 1/6 = 1/12.
Question 3
Two coins were flipped together 50 times. Based on these results, what is the experimental probability of "two heads"? Give a fraction.
50 flips of two coins Result Count Two heads 10 One head, one tail 19 Two tails 21 answer box
1/5
Hint: Experimental probability = times it happened ÷ total trials = 10/50 = 1/5.
Question 4
Two spinners are each half red and half blue. Maya spun both 25 times, and both landed on red 7 times. What is the experimental probability of "both red" as a percent?
answer box%
28 %
Hint: Experimental probability = 7/25 = 0.28 = 28%. Compare it with the theoretical probability: 1/2 × 1/2 = 1/4 = 25%.
Question 5
Sam flips a coin 10 times and gets 7 heads. What does this show?
- The next flip is more likely to be tails
- The coin will land heads 70% of the time from now on
- Experimental results can differ from the theoretical probability
- The theoretical probability of heads is 7/10
Experimental results can differ from the theoretical probability
Hint: Theoretical P(heads) is still 1/2. Ten flips is a small experiment, so 7 heads isn't surprising, and the coin has no memory.
Question 6
Suppose you flip a coin and roll a standard die (1 to 6), and repeat this 300 times. About how many times would you expect to get heads and a 6?
answer box
25
Hint: P(heads and a 6) = 1/2 × 1/6 = 1/12. Expected: 1/12 × 300 = 25 times.