Good luck, rather than good genes, may be the key reason why some people are protected from certain cancers while others develop the disease, according to a new study.

Two-thirds of adult cancers, say the researchers from the Johns Hopkins Kimmel Cancer Center in the United States, are caused by random mutation in the tissue cells during the ordinary process of stem cell division. In the other third, our genetic inheritance and lifestyles are the main factors.

The scientists have created a mathematical model which, they say, shows it is wrong to assume that there are such things as “good genes” that may prevent us getting cancer even though we smoke, drink heavily and carry excessive weight.

“All cancers are caused by a combination of bad luck, the environment and heredity, and we’ve created a model that may help quantify how much of these three factors contribute to cancer development,” says Bert Vogelstein, the Clayton professor of oncology at the Johns Hopkins University school of medicine and one of the authors of the paper published in the journal Science. “Cancer-free longevity in people exposed to cancer-causing agents, such as tobacco, is often attributed to their ‘good genes’, but the truth is that most of them simply had good luck.”

The scientists looked at how often stem cell division, the normal process of cell renewal, takes place in 31 different tissue types, to find out whether the sheer number of divisions can lead to more mistakes – or DNA mutations – occurring. They did not look at tissues from two of the commonest forms of cancer – breast and prostate – which are known to have particular environmental triggers, such as obesity. These were not included because they could not find reliable data on the normal division rate of stem cells in these tissues.

“Our study shows, in general, that a change in the number of stem cell divisions in a tissue type is highly correlated with a change in the incidence of cancer in that same tissue,” said Vogelstein. One example, he says, is in colon tissue, which undergoes four times more stem cell divisions than small intestine tissue in humans. Likewise, colon cancer is much more prevalent than small intestinal cancer.

It could be argued, they say, that the colon is exposed to more environmental factors than the small intestine – but they point out that the opposite is true for mice, which have more stem cell divisions and a higher rate of cancer in their small intestines than in their colon.

The scientists say that bad luck plays a stronger role in some cancers than in others. In two-thirds of the cancers – 22 cancer types – random mutations in genes that drive cancer could explain why the disease occurred. The other nine cancers occurred more often than the random mutation rate would predict, suggesting that inherited genes or lifestyle factors were the main cause. They included lung cancer, where smoking is the major cause, and skin cancer, which can be triggered by sun exposure.

Speaking on the BBC Radio 4 Today programme on Friday, co-author biomathematician Dr Cristian Tomasetti, also from Johns Hopkins University, said: “I’m not claiming any cancers, overall across the population, are the result of pure chance, but what I am claiming is there are some tissues – for example blood cancer – where there is very little evidence of any hereditary or environmental factor.”

To explain the study, Tomasetti offered an example. He said: “Let’s say my parents smoked all their lives and they never got lung cancer. If I strongly believed cancer was only environment, or the genes that are inherited, then since my parents didn’t get cancer I may think I must have good genes.

“So I would think it would be OK to smoke. On the contrary, our study says no, my parents were just extremely lucky and played a very dangerous game.”