Probability I · Probability spaces, axioms, and rigorous counting
A spinner has four equally likely sectors, labelled A₁,A₂,B,C
Problem
A spinner has four equally likely sectors, labelled \(A_1,A_2,B,C\). Spin it twice independently, recording both sector labels. For a second record, erase the subscripts and ignore the order of the two letters. Give an equally likely elementary sample space for the experiment. Find the probabilities of the six possible unordered letter records \(AA,AB,AC,BB,BC,CC\). Calculate the probability that the two sector labels agree and the probability that the two letters agree. Explain why assigning probability \(1/6\) to each unordered letter record would model a different experiment.
Hint
Before erasing anything, how many choices are available at each spin?
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