The type of reinforcement schedule that is illustrated is: fixed-ratio schedule.
Fixed-ratio schedule is a form of partial reinforcement, whereby a response is rewarded or the reinforcement is delivered only when a number of specified responses has been exhibited.
The reinforcement in the scenario given in the question is a free coffee drink. The number of responses required for reinforcement to be delivered is nine coffee drinks purchase.
Therefore, the type of reinforcement schedule that is illustrated is: fixed-ratio schedule.
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