7th grade · Math · Unit 7 of 18
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.
Alabama Course of Study content standard: 7.13; 7.14; 7.16 · probability of chance events, probability models 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 Alabama
In the Alabama Course of Study, this is unit 7 of 18 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.
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
Sam flips a coin 10 times and gets 7 heads. What does this show?
- The coin will land heads 70% of the time from now on
- The theoretical probability of heads is 7/10
- Experimental results can differ from the theoretical probability
- The next flip is more likely to be tails
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 2
Two coins were flipped together 40 times. Based on these results, what is the experimental probability of "two heads"? Give a fraction.
40 flips of two coins Result Count Two heads 9 One head, one tail 19 Two tails 12 answer box
9/40
Hint: Experimental probability = times it happened ÷ total trials = 9/40.
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 flip a coin and roll a standard die (1 to 6). What is the probability of getting tails and an even number? Give a fraction.
answer box
1/4
Hint: The events are independent, so multiply: P(tails) × P(an even number) = 1/2 × 3/6 = 3/12 = 1/4.
Question 5
The table shows every outcome of flipping a coin (H or T) and rolling a die. How many outcomes show heads and an even number?
Coin 1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6 answer box
3
Hint: Find the matching cells: H2, H4, H6. That's 3 of the 12 outcomes.
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 1?
answer box
25
Hint: P(heads and a 1) = 1/2 × 1/6 = 1/12. Expected: 1/12 × 300 = 25 times.