Patients with cancer are prone to have blood clots, which are usually treated with blood thinners. The main complication of blood thinners is bleeding. This is especially a concern when the number of platelets in the blood is lower than 50,000 per microliter. The role of platelets is to stop bleeding, so when the number of platelets is low, patients are at a higher risk of bleeding. Cancer patients are prone to have lower platelet numbers due to cancer therapies and/or cancer itself. It is not clear what the best treatment is for cancer patients who need blood thinners for a blood clot but have low platelet counts. The investigators plan to do a small study called a pilot study to help plan for a larger study in such patients. In the pilot study, investigators will include 50 patients with cancer, low platelet counts, and a blood clot diagnosed within 4 weeks. Patients will be randomly assigned to one of the two treatment strategies: the full dose of blood thinners along with platelet transfusion or a reduced dose of blood thinners without platelet transfusion. The investigators will follow all patients for 90 days. If this pilot study is successful, it will help lead to a much larger trial, which will provide important information on the best treatment strategy in these patients.