This thesis analyzes the occurence of the quantum Zeno effect in a qubit in different situations. A system with a particle with spin 1/2, which represents a qubit, and detector is considered. The detector is modeled by a coordinate q, which has a Gaussian distribution with dispersion σ. There is the free evolution of the qubit and the interaction with the detector. Moreover, there are calculated algebraic expressions for the probabilities of the qubit to be in one of its states at certain moments in time by considering the wave function and density matrix at that time and consequently tracing out the detector coordinate q. Furthermore, there is done an analysis using plots of the evolution of these probabilities in time for different situations. In the situation with one continuous measurement and no free evolution, the qubit remains in its initial state, as expected.In the situation where periods of only free evolution and only measurements alternate, the probabilities keep the same value during the measurement, so then the evolution of the system freezes, and the probabilities evolve in a sine form during the free evolution, in line with the expectation.To neglect free evolution during the measurement, tm << tev is assumed, so there are no series of fast subsequent measurements or a continuous measurement. In this case, the quantum Zeno effect does not occur.Furthermore, we consider the situation where periods of only free evolution and periods with a measurement during free evolution alternate. Now the oscillations continue in time, due to the ongoing free evolution. The larger the influence of the interaction between the qubit and detector during the measurement and the smaller the influence of the magnetic field of the free evolution, the higher the equilibirium position of the oscillations of the probability for the qubit to remain in its initial state is in time. Moreover, the amplitude of these oscillations is smaller. However, due to the free evolution the qubit always has a probability to undergo a transition to its other state. The continuous measurement does not freeze the evolution of the system totally. The quantum Zeno effect does not occur.In the situation where the dispersion σ of the detector coordinate q goes to 0, there is a perfect measurement. The larger σ, the larger the measurement error in the detector resulting in dissipation of the system. The oscillations of the probabilities damp in time.Recommendations for further research include plotting the evolution of the probabilities for a longer period in time with another integration tool. Also, it would be interesting to work out the assumptions done in this analysis to more realistic conditions. Furthermore, another distribution of the detector coordinate q and other qubit states might be interesting to work out in follow-up research.