L4 · Experimental vs theoretical probability
“I can run or read a probability experiment, calculate the experimental probability from the results, compare it with the theoretical probability from the sample space, and explain why more trials usually bring the two closer together.”
A spinner has 4 equal sections: A, B, C, D. It is spun 40 times. Section A lands 12 times. Step 1: Theoretical probability (from the sample space - no trials needed): P(A) = 1/4 = 25%. Step 2: Experimental probability (from the results): P(A) = favourable trials / total trials = 12/40 = 3/10 = 30%. Step 3: Compare: 30% (experiment) vs 25% (theory). They are close, but not equal - and that is normal. Trials are affected by chance; 40 spins is not enough to force the results to match the theory exactly. Step 4: The two numbers answer different questions. Theory says what SHOULD happen in the long run; the experiment says what DID happen this time. Model both ways: the tally chart of the 40 spins, AND both probabilities marked on a 0%-100% number line - 25% and 30%, near each other but not on top of each other. Say it plainly: experimental probability never rewrites the theory. It estimates it.
The experiment gave 30% but the theory says 25%. What is the best explanation?
A coin is flipped 50 times and lands on heads 27 times. Find the experimental P(heads) and compare it with the theoretical P(heads). -> Experimental: 27/50 = 54%. Theoretical: 1/2 = 50%. Close, but not equal.
"A die is rolled 12 times and a 5 comes up twice. Experimental P(5) = 2/12 = ___. The theoretical P(5) is ___." -> 2/12 = 1/6; theoretical 1/6 - this time they agree (small experiments sometimes land exactly on the theory, by chance)
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.