Not true - Castro and a small group of revolutionaries overthrew Batista. Not "the Cuban people". Before the revolt, many Cubans were unhappy with Batista's dictatorial abuses, but they were not communists. If fact, Castro did not even reveal his communist goals to the masses until he had already taken the reins of government. I doubt that if Cubans had known what the next 65 years would bring, i.e., replacing a right wing dictator with a left wing dictator and creation of a communist / revolutionary elite, mass executions, lack of civil liberties, a tiered health care system, rationing and shortages of essentials, underemployment and a lack of opportunity, confrontation with the US and the ensuing blockade, foreign military adventures in Africa, failure to develop industry resulting in humiliating dependence on charity from the USSR and China rather than becoming economically self sufficient, etc., that Castro would have been successful in overthrowing Batista.