Likelihood of Events: Certain, Uncertain, More and Less Likely
Warm-up
Show a spinner with half red and half blue. Is red more likely, blue more likely, or equally likely? (Equally likely: same area.) Show a spinner with 3/4 red and 1/4 blue. Now which is more likely? (Red.) Why? (More of the spinner is red.) Evidence from the visual grounds the judgment.
Explore
Marble bag experiment: each pair has a bag with a known number of coloured marbles (e.g., 6 red, 2 blue). Predict: if you draw without looking, is red or blue more likely? Why? Draw 20 times, replacing each time. Record results. Compare to prediction. Was the data consistent with the likelihood?
Consolidate
Practice
Students predict and test 4 probability experiments (spinners, marbles, dice), recording predictions, results, and whether results matched predictions. Exit ticket: name one pair of equally likely events and explain why they are equally likely.
Exit ticket
Students predict and test 4 probability experiments (spinners, marbles, dice), recording predictions, results, and whether results matched predictions. Exit ticket: name one pair of equally likely events and explain why they are equally likely.
Equally likely: both have 4 marbles out of 12. The same fraction (4/12 = 1/3) of the bag is each colour. No colour has an advantage.
No: a fair coin has no memory. Each flip is equally likely to be heads or tails regardless of previous results. This is the gambler's fallacy, and addressing it directly is important for critical thinking.