The statement that mutations are random is both profoundly true and profoundly untrue at the same time. The true aspect of this statement stems from the fact that, to the best of our knowledge, the consequences of a mutation have no influence whatsoever on the probability that this mutation will or will not occur. In other words, mutations occur randomly with respect to whether their effects are useful. Thus, beneficial DNA changes do not happen more often simply because an organism could benefit from them. Moreover, even if an organism has acquired a beneficial mutation during its lifetime, the corresponding information will not flow back into the DNA in the organism's germline. This is a fundamental insight that Jean-Baptiste Lamarck got wrong and Charles Darwin got right.
However, the idea that mutations are random can be regarded as untrue if one considers the fact that not all types of mutations occur with equal probability. Rather, some occur more frequently than others because they are favored by low-level biochemical reactions. These reactions are also the main reason why mutations are an inescapable property of any system that is capable of reproduction in the real world. Mutation rates are usually very low, and biological systems go to extraordinary lengths to keep them as low as possible, mostly because many mutational effects are harmful. Nonetheless, mutation rates never reach zero, even despite both low-level protective mechanisms, like DNA repair or proofreading during DNA replication, and high-level mechanisms, like melanin deposition in skin cells to reduce radiation damage. Beyond a certain point, avoiding mutation simply becomes too costly to cells. Thus, mutation will always be present as a powerful force in evolution
