7th grade · Math · Unit 6 of 20
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.
New York State Learning Standards learning standard: NY-7.SP.8 · probabilities of compound events with organized lists, tables and simulation
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 New York
In the New York State Learning Standards, this is unit 6 of 20 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 50 times. Based on these results, what is the experimental probability of "one head, one tail"? Give a fraction.
50 flips of two coins Result Count Two heads 12 One head, one tail 27 Two tails 11 answer box
27/50
Hint: Experimental probability = times it happened ÷ total trials = 27/50.
Question 2
Which pair of events is independent?
- Flipping a coin, then rolling a die
- 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
- Taking a marble from a bag, then taking another without putting the first back
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 3
You spin this spinner (5 equal sections) and flip a coin. What is P(yellow and heads)?
- 1/5
- 2/7
- 1/10
- 7/10
1/10
Hint: P(yellow) = 1/5 and P(heads) = 1/2. The events are independent, so multiply: 1/5 × 1/2 = 1/10.
Question 4
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 5
Two spinners are each half red and half blue. Leo spun both 50 times, and both landed on red 16 times. What is the experimental probability of "both red" as a percent?
answer box%
32 %
Hint: Experimental probability = 16/50 = 0.32 = 32%. Compare it with the theoretical probability: 1/2 × 1/2 = 1/4 = 25%.
Question 6
Suppose you flip a coin and roll a standard die (1 to 6), and repeat this 60 times. About how many times would you expect to get heads and a 1?
answer box
5
Hint: P(heads and a 1) = 1/2 × 1/6 = 1/12. Expected: 1/12 × 60 = 5 times.