Random variables X1,…,XkX_1,…,X_k are mutually independent if, for all possible values v1,…,vkv_1,…,v_k, Pr[X1=v1,...,Xk=vk]=Pr[X1=v1]⋅...⋅Pr[Xk=vk]\mathrm{Pr}[X_1 = v_1, ..., X_k = v_k] = \mathrm{Pr}[X_1 = v_1]\cdot ... \cdot \mathrm{Pr}[X_k = v_k]
Strictly stronger than Pairwise independence; mutual independence implies pairwise independence, but pairwise independence does not imply mutual independence.
See Types of Independence.