7th grade · Math · Unit 6 of 15
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.
Minnesota K-12 Academic Standards benchmark: 7.1.2.4; 7.1.2.6 · sample spaces and probabilities of 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 Minnesota
In the Minnesota K-12 Academic Standards, this is unit 6 of 15 in 7th grade Math, after Circles 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.
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 60 times. Based on these results, what is the experimental probability of "two tails"? Give a fraction.
60 flips of two coins Result Count Two heads 16 One head, one tail 26 Two tails 18 answer box
3/10
Hint: Experimental probability = times it happened ÷ total trials = 18/60 = 3/10.
Question 2
Two spinners are each half red and half blue. Priya spun both 25 times, and both landed on red 5 times. What is the experimental probability of "both red" as a percent?
answer box%
20 %
Hint: Experimental probability = 5/25 = 0.2 = 20%. Compare it with the theoretical probability: 1/2 × 1/2 = 1/4 = 25%.
Question 3
Suppose you flip a coin and roll a standard die (1 to 6), and repeat this 120 times. About how many times would you expect to get tails and a 6?
answer box
10
Hint: P(tails and a 6) = 1/2 × 1/6 = 1/12. Expected: 1/12 × 120 = 10 times.
Question 4
You flip a coin and roll a standard die (1 to 6). What is the probability of getting tails and a number less than 3? Give a fraction.
answer box
1/6
Hint: The events are independent, so multiply: P(tails) × P(a number less than 3) = 1/2 × 2/6 = 2/12 = 1/6.
Question 5
You spin this spinner (4 equal sections) and flip a coin. What is P(blue and heads)?
- 3/4
- 1/8
- 2/6
- 1/4
1/8
Hint: P(blue) = 1/4 and P(heads) = 1/2. The events are independent, so multiply: 1/4 × 1/2 = 1/8.
Question 6
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.