Cell fate regulation is an open problem whose comprehension impacts several areas of the biosciences. DNA damage induces cell cycle checkpoints that activate the p53 pathway to regulate cell fate mechanisms such as apoptosis or senescence. Experiments with different cell types show that the p53 pathway regulates cell fate through a switch behavior in its dynamics. For low DNA damage the pathway presents an oscillatory pattern associated with intense DNA damage repair while for high damage there are no oscillations and either p53 concentration increases inducing apoptosis or the cell enters a senescence state. Apoptosis and senescence phenotypes seem to have compensatory functions in tissues and the microRNA 16-1 (miR-16) is involved in the regulation of the fate between both phenotypes in cancer cells. To investigate the regulation of cell fate we developed a logical model of the G1/S checkpoint in DNA damage response that takes into account different levels of damage and contemplates the influence of miR-16 through its positive feedback loop formed with p53 and Wip1. The model reproduces the observed cellular phenotypes in experiments: oscillatory (for low DNA damage) regulated by negative feedback loops involving mainly p53 and Mdm2 and apoptotic or senescent (for high DNA damage) regulated by the positive p53/Wip1/miR-16 feedback loop. We find good agreement between the level of DNA damage and the probability of the phenotype produced according to experiments. We also find that this positive feedback makes senescent and apoptotic phenotypes to be determined stochastically (bistable), however controlling the expression level of miR-16 allows the control of fate determination as observed experimentally.