Motivated by the rationing of medicine during the pandemic, we determine the probability that a scarce resource is allocated based on its relationship to a conditional probability from a weighted lottery. Using the binomial theorem and some elementary combinatorics, we determine the probability of receiving the medicine when there are different types of patients. When there is just one type of patient so that every patient is treated the same, counterintuitively, a patient may have a higher probability of receiving the medicine, if the conditional probability is less.