This study investigated first-year undergraduate statistics students' statistical problem-solving skills on the probability of the union of two events, conditional probability, binomial probability distribution, probabilities for x-limits using the z-distribution, x-limit associated with a given probability for a normal distribution, estimating the y-value using a regression equation, and hypothesis testing for a single population mean when a population standard deviation is unknown. The study was a descriptive case study and employed a mixed-method research approach. Data were collected through content analysis of a statistics course examination script of 120 first-year undergraduate students of statistics in an open distance-learning university in South Africa. Polya's Model of Problem Solving was used as the framework of analysis. The study revealed that the students, in general, had poor statistical problem-solving skills.