Grade 7 · Math · Unit 16 of 16
Probability
Chances of two events
What your child practises
Listing outcomes of two independent events (like a coin and a die), finding theoretical probabilities by multiplying, and comparing them with experimental results.
Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Statistics and Probability · probability as ratios, fractions and percents, and two independent events
How we explain it
Children can open this short lesson before they practise.
- Probability = favourable 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
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 spin this spinner (5 equal sections) and flip a coin. What is P(orange and tails)?
- 1/10
- 2/7
- 7/10
- 1/5
1/10
Hint: P(orange) = 1/5 and P(tails) = 1/2. The events are independent, so multiply: 1/5 × 1/2 = 1/10.
Question 3
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 tails and a 6?
answer box
5
Hint: P(tails and a 6) = 1/2 × 1/6 = 1/12. Expected: 1/12 × 60 = 5 times.
Question 4
Two spinners are each half red and half blue. Maya spun both 20 times, and both landed on red 4 times. What is the experimental probability of "both red" as a percent?
answer box%
20 %
Hint: Experimental probability = 4/20 = 0.2 = 20%. Compare it with the theoretical probability: 1/2 × 1/2 = 1/4 = 25%.
Question 5
Two coins were flipped together 60 times. Based on these results, what is the experimental probability of "one head, one tail"? Give a fraction.
60 flips of two coins Result Count Two heads 15 One head, one tail 32 Two tails 13 answer box
8/15
Hint: Experimental probability = times it happened ÷ total trials = 32/60 = 8/15.
Question 6
Sam flips a coin 10 times and gets 7 heads. What does this show?
- Experimental results can differ from the theoretical probability
- The next flip is more likely to be tails
- 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
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.