7th grade · Math · Unit 7 of 16
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.
Arizona Academic Standards learning standard: 7.SP.C.5; 7.SP.C.7 · 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 Arizona
In the Arizona Academic Standards, this is unit 7 of 16 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: Arizona 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 flip a coin and roll a standard die (1 to 6). What is the probability of getting tails and a 6? Give a fraction.
answer box
1/12
Hint: The events are independent, so multiply: P(tails) × P(a 6) = 1/2 × 1/6 = 1/12.
Question 2
As you do more and more trials, the experimental probability usually…
- gets farther from the theoretical probability
- stops changing after 10 trials
- always equals exactly 1/2
- gets closer to the theoretical probability
gets closer to the theoretical probability
Hint: Small experiments can be lopsided. With many trials, results tend to settle near the theoretical probability.
Question 3
You roll a standard die (1 to 6) and spin a spinner with 4 equal sections. How many different outcomes are possible?
answer box
24
Hint: Each of the 6 results of the first event can pair with each of the 4 results of the second: 6 × 4 = 24 outcomes. A tree diagram or table shows them all.
Question 4
You spin this spinner (4 equal sections) and flip a coin. What is P(orange and tails)?
- 2/6
- 1/8
- 1/4
- 3/4
1/8
Hint: P(orange) = 1/4 and P(tails) = 1/2. The events are independent, so multiply: 1/4 × 1/2 = 1/8.
Question 5
Two coins were flipped together 50 times. Based on these results, what is the experimental probability of "two tails"? Give a fraction.
50 flips of two coins Result Count Two heads 15 One head, one tail 26 Two tails 9 answer box
9/50
Hint: Experimental probability = times it happened ÷ total trials = 9/50.
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.