Looks trivial until you second-guess yourself mid-answer.
Recognize that each rider's coupon usage is an independent Bernoulli trial with probability P. The total cost is $5 times the number of riders who use the coupon, so the expected total cost is $5 * N * P. State this clearly and then discuss assumptions and potential extensions.
Pro tip: Mention that this is a linearity of expectation problem and that the result holds regardless of dependence between riders, but in practice, you'd also consider factors like coupon stacking, expiration, and incremental lift to assess true cost.
Let X_i be an indicator variable for whether rider i uses the coupon, with P(X_i = 1) = P. The total cost C = 5 * sum_{i=1}^N X_i.
Compute E[C] = 5 * sum_{i=1}^N E[X_i] = 5 * N * P. This avoids needing to know the distribution of the sum.
The expected total cost is $5NP. For example, if N=10,000 and P=0.1, expected cost is $5,000.
Note that this assumes independence and identical P, but linearity holds even without independence. In reality, consider that coupons may be used on orders of varying sizes, and the cost might be offset by increased revenue.
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