A child born in the United States this year will have greater than a one in three chance of eventually developing an invasive cancer, and, depending on sex and race, a one in four or five chance of dying from it.

According to a report in the January-February issue of Ca, the American Cancer Society's journal for clinicians, the probablility of dying from cancer is greater for this year's newborns than for those born a decade ago, in part because fewer people die from heart attack and stroke.

Herbert Seidman, assistant vice president of the Cancer Society and one of the report's authors, says that the projected increases in certain cancers come as the result of "our ability on the one hand to accomplish near miracles. The decrease in cardiovascular death rate is certainly a near miracle compared to the situation 15 years ago. But this gives us more people living to get cancer."

Prostate cancer, for example, may remain undetected for many years, he says, and may only become clinically significant for the male population as more men with healthier cardiovascular systems live to a greater age. "Then, of course, it becomes a problem of greater proportions."

Seidman and his colleagues used the recently released National Cancer Institute figures from the Surveillance, Epidemiology and End Results (SEER) program, which began its study in 1973 of more than 10 percent of the population, monitoring cancer incidence, treatment and mortality or survival.

The ACS epidemiologists also used some unpublished data from the National Center for Health Statistics concerning mortality data for 1981 as well as life tables for 1975. From these, the ACS study projected and extrapolated the incidences and deaths from virtually all "invasive" cancers, excluding such non-invasive cancers as basal-cell and squamous-cell skin cancers. (These were also excluded from the SEER study.)

Some of the findings:

* White males have the greatest probability of developing some kind of cancer, followed by black males, white women and, last of all, black women. The probabilities have increased in all four groups since 1975, with the differences between the races decreasing slightly.

* Black males have a higher probability of developing the so-called "life style-related" cancers such as those of the mouth, pharynx, esophagus, larynx, lung and prostate. These are cancers that may be linked to smoking, excessive alcohol consumption, poor diets and, in some cases, says Weidmen, "the dirty end of the stick in terms of occupational exposure."

* The most common cancers for males of both races will continue to be cancers of the lung, prostate and colon-rectum, the ACS study predicts.

* The most common cancers for women of both races will be cancers of the breast, colon-rectum, uterus and lung. The chances of developing these cancers increased during each of the three time periods covered in the study.

By the end of this year, lung cancer is expected to join breast cancer as the leading cause of cancer deaths in women.

* White women have, and will continue to have, according to these projections, a higher probability of developing breast cancer than black women.

* Black women have a higher probability of developing cancers of the esophagus and cervix than white women.

* The probability of developing stomach cancer is decreasing for women of both races.

The projections, says Weidman, are intended "as an overview, not as something with precise emphasis on figures. To some extent it is a kind of philosophical work supported by numbers. It was designed to show the direction of health problems as other causes of death are overcome and the population grows older.

"We would hope that as we increase life span, we also increase quality of life. We don't mean to scare people with these things, but there are challenges and there are problems."

The Ca authors also cite SEER data indicating five-year survival rates for about half of all newly diagnosed cancer patients. However, this conclusion has been criticized as misleadingly optimistic. Despite advances in the treatment of some cancers -- such as childhood leukemias, Hodgkin's disease and cervical cancer -- survival rates have not been greatly increased in some of the major cancers, notably lung and breast.