Even in response to simple tasks such as hand movement, human brain activity shows remarkable inter-subject variability. Recently, it has been shown that individual spatial variability in fMRI task responses can be predicted from measurements collected at rest; suggesting that the spatial variability is a stable feature, inherent to the individual's brain. However, it is not clear if this is also true for individual variability in the spatio-spectral content of oscillatory brain activity. Here, we show using MEG (N = 89) that we can predict the spatial and spectral content of an individual's task response using features estimated from the individual's resting MEG data. This works by learning when transient spectral 'bursts' or events in the resting state tend to reoccur in the task responses. We applied our method to motor, working memory and language comprehension tasks. All task conditions were predicted significantly above chance. Finally, we found a systematic relationship between genetic similarity (e.g. unrelated subjects vs. twins) and predictability. Our approach can predict individual differences in brain activity and suggests a link between transient spectral events in task and rest that can be captured at the level of individuals.