Alcoholics and heavy drinkers score higher on measures of impulsivity than nonalcoholics and light drinkers. This may be because of factors that predate drug exposure (e.g. genetics). This study examined the role of genetics by comparing impulsivity measures in ethanol-naive rats selectively bred based on their high [high alcohol drinking (HAD)] or low [low alcohol drinking (LAD)] consumption of ethanol. Replicates 1 and 2 of the HAD and LAD rats, developed by the University of Indiana Alcohol Research Center, completed two different discounting tasks. Delay discounting examines sensitivity to rewards that are delayed in time and is commonly used to assess ‘choice’ impulsivity. Probability discounting examines sensitivity to the uncertain delivery of rewards and has been used to assess risk taking and risk assessment. High alcohol drinking rats discounted delayed and probabilistic rewards more steeply than LAD rats. Discount rates associated with probabilistic and delayed rewards were weakly correlated, while bias was strongly correlated with discount rate in both delay and probability discounting. The results suggest that selective breeding for high alcohol consumption selects for animals that are more sensitive to delayed and probabilistic outcomes. Sensitivity to delayed or probabilistic outcomes may be predictive of future drinking in genetically predisposed individuals.