The appellant, Terri Rachals, a nurse employed in the Surgical Intensive Care Unit of the Phoebe Putney Memorial Hospital, of Albany, Georgia, was indicted and tried on six counts of murder and twenty counts of aggravated assault, allegedly caused by the administration of potassium chloride to patients in the intensive care unit. The jury returned verdicts of “not guilty” on all murder charges, and 19 counts alleging aggravated assault. Mrs. Rachals was found “guilty but mentally ill” of aggravated assault, with intent to murder, of Sam Bentley, by injecting potassium chloride into a bag of fresh frozen plasma, which was then introduced into Bentley’s body while he was a patient in the Intensive Care Unit of the Phoebe Putney Hospital.
Following an unusual increase in the number of cardiac arrests of patients in the Phoebe Putney Hospital during the latter part of 1985, investigations were conducted by the Georgia Department of Human Resources and the Georgia Bureau of Investigation. Following these investigations, Rachals was arrested for the various charges of murder *421and aggravated assault. Held,'.
1. In a hearing to determine the voluntariness of a statement Rachals made to the investigating GBI agents, a Dr. Turner was allowed to testify that when he spoke with Rachals shortly after her confrontation by the GBI agents, Rachals appeared to be able to tell right from wrong. Rachals contends that this testimony violated the psychiatrist-patient privilege established by OCGA § 24-9-21.
Before the psychiatrist/patient communications privilege arises under OCGA § 24-9-21, a relationship of psychiatrist and patient must exist, to the extent that treatment was given or contemplated. Massey v. State, 226 Ga. 703 (177 SE2d 79) (1970). The most realistic view of the evidence simply is that the appellant’s real concern was more to avoid the immediate reality of spending the night in jail, rather than seeking psychiatric treatment. Certainly the appearance of the psychiatrist resulted from the efforts of others.
The record shows that following her statement to the GBI agents, the appellant asked the head nurse to call Dr. Calhoun, in whom she had previously confided about her emotional and domestic problems. In response to the appellant’s remark that she would kill herself if she had to go to jail, Dr. Calhoun replied that they would try to get her some help. Dr. Turner was then summoned, and, after talking with the appellant for a few minutes, asked her if she would consent to a voluntary admission into the psychiatric ward. Not surprisingly, the appellant readily assented.
She remained in the ward only until the following morning. It does not appear that she received treatment of any kind during this brief retreat to the psychiatric ward, and upon her release (in the custody of the police) she never again sought the services of Dr. Turner. Under these circumstances, no psychiatrist/patient relationship was created because (1) the appellant certainly was not seeking out psychiatric care in the usual sense of the term; and (2) no real treatment was given or contemplated. Accordingly, no communications privilege restricted the admissibility of Dr. Turner’s testimony.
In any event, even if a psychiatrist/patient relationship existed between Dr. Turner and the appellant, any error in the admission of Dr. Turner’s testimony was harmless. The objectionable testimony was Dr. Turner’s opinion that the appellant appeared to know right from wrong at the time he talked with her. During the trial, two other psychiatrists, who had evaluated the appellant, also testified that in their opinions the appellant’s emotional problems did not interfere with her ability to tell right from wrong. Thus, because Dr. Turner’s testimony was cumulative of other, properly-admitted evidence, reversal is inappropriate. See Wilson v. Bonner, 166 Ga. App. 9 (5) (303 SE2d 134) (1983); Caston v. State, 178 Ga. App. 752 (344 SE2d 725) (1986).
*4222. The taped statement of Rachals to the GBI agents is not subject to the objection that it is inadmissible because it is “hearsay.” Sanders v. State, 246 Ga. 42 (268 SE2d 628) (1980); Thomas v. State, 240 Ga. 393 (2) (242 SE2d 1) (1977); Stanley v. State, 240 Ga. 341 (3) (241 SE2d 173) (1977). Further, whether an accused is mentally capable of, and did in fact make a knowing and intelligent waiver of her Miranda rights, is a factual and credibility issue for the trial court and will not be disturbed on appeal unless clearly erroneous. Evans v. State, 176 Ga. App. 818, 820 (338 SE2d 48) (1985).
3. Appellant also enumerates as error the testimony of Dr. Adelle Franks, which by inference could be interpreted to mean that “Terri Rachals was, by odds of five out of nine, probably guilty.” Dr. Franks was an epidemiologist, from the U. S. Center for Disease Control, on loan to the Georgia Department of Human Resources. The Georgia DHR had requested assistance in evaluating the increase in the number of cardiac arrests occurring in the Phoebe Putney Hospital. Dr. Franks went to the hospital in December 1985, and examined the hospital’s records for the entire year previous to November 1985. In three of those months, the hospital had experienced no cardiac arrests. In two months, four cardiac arrests had occurred in each month. Accordingly, Dr. Franks stated that the hospital should have between zero and four cardiac arrests in a normal month. However, in the month of November 1985, eleven cardiac arrests had occurred on the 3:00 o’clock to 11:00 o’clock shift. The probability of this occurring “by chance alone is less than one in a trillion.” In the month of November, five cardiac arrests had occurred in one day and one patient had a total of eight cardiac arrests in that one month. Dr. Franks listed all cardiac arrest patients for the period investigated and the primary nurse on duty with that patient. Rachals was the primary nurse for 11 cardiac arrest patients in the month of November. No other nurse was the primary care nurse for more than one cardiac arrest patient. Dr. Franks charted all 24 nurses for that month and the number of cardiac arrests that occurred on their shift, and those that occurred when they were not on shift to calculate a “rate ratio.” The “rate ratio” for most nurses was around one, while the “rate ratio” for Rachals “was 26.6, which means that in 26.6 times, it was more likely that a cardiac arrest would occur while she was on duty than when she was not on duty. . . . [T]he rate ratio show infinitely large and unmeasurable [sic] because all of the cardiac arrests that occurred on the 3:00 o’clock to 11:00 o’clock shift occurred while she was on duty.” Rachals’s counsel contends that this testimony impermissibly invaded the province of the jury, in that it concluded that if a crime occurred while Rachals was on duty, the odds were 26.6 to 1 that she did it.
GBI Agent Sweat testified that of the 19 cardiac arrests that occurred during the investigative period, Rachals was charged with *423every cardiac arrest which occurred while she was on duty. Since she was not present when eight occurred, she was not charged with them. Six cardiac arrests occurred on one day, November 24, although it was not normal for more than four cardiac arrests to occur within a one-month period. Rachals was not charged with three of them since she was not present. Dr. Franks admitted that four cardiac arrests within a one-month period would be considered normal and she could not tell you which of any of the cardiac arrests that occurred when Rachals was on duty could be considered to be normally expected.
In Williams v. State, 251 Ga. 749 (312 SE2d 40) (1983), the Supreme Court was faced with an allegation of error “in permitting a state’s expert witness to discuss mathematical probabilities concerning the fiber evidence and in permitting the prosecutor to argue mathematical probabilities to the jury.” Id. at 786. The court found no error “as experts are permitted to give their opinions, based upon their knowledge, including mathematical computations.” Id. This enumeration was not exhaustively discussed, because of the numerous allegations of error in the Williams case, but it appears to sanction “mathematical probabilities concerning . . . evidence,” including evidence which circumstantially permits an inference of guilt. While no one would doubt the admissibility of the raw data to a jury about what acts occurred on which nurses’ shifts, we have serious reservations about mathematical computations as to the probability of guilt of an accused person. However, we are constrained to follow Williams, supra, and find no reversible error under the facts of this case.
Other jurisdictions have been even less open to the admissibility of such matters of statistical and mathematical probability. In People v. Collins, 66 Cal. Rptr. 497 (438 P2d 33) (1968), for example, the Supreme Court of California disallowed the use of a mathematical formula to establish the presence of the two defendants at the scene of the crime. That court determined that the statistical analysis was invalid due to the large number of variables that could be duplicated in the uncontrolled environment. There the odds were listed as one in twelve million that the asserted fact occurred by chance, as compared to one in a trillion in the case sub judice. For a simple, lucid, and informative guide to mathematical, statistical analysis, and suggested formulas advanced for alleged arithmetical accuracy, this writer invites reference to the Appendix contained in Collins.
In the instant case, however, the number of variables was limited in the controlled situation, and the statistics were not derived from a random sampling. Rather, hospital records established the average number of cardiac arrests for the entire year prior to November 1985, when the dramatic increase in the number of cardiac arrests was noticed. The potential for analytical error that was apparent in Collins is absent in the instant case. When in doubt, evidence of this type *424should be admitted, unless based on sheer speculation, Woods v. Andersen, 145 Ga. App. 492, 496 (243 SE2d 748) (1978), although it may be totally rejected by the jury. While “these observations are made to emphasize the caution with which the courts should greet such presentations of statistical probability in criminal proceedings,” Brooks v. State, 171 Ga. App. 55, 57 (318 SE2d 785) (1984), the testimony was admissible in this case, for whatever value the jury assigned it.
4. Rachals also contests the sufficiency of the evidence to show her guilt as to the aggravated assault upon Sam Bentley. Dr. Douglas Calhoun was Bentley’s attending physician. While at a meeting he received word that Bentley’s heart rhythm and blood pressure did not appear to be stable. He immediately went to his bedside and after examination ordered fresh frozen plasma to be administered. Janice Thomas was the primary nurse for Bentley but Rachals went to the lab and procured the fresh frozen plasma. Thomas does not remember which nurse hung the plasma. In her recorded statement to GBI Agent Sweat, Rachals told him Mr. Bentley asked her to “let him die.” He was “very, very ill also. His skin was sloughing off and he was just laying there suffering and he’d just look at you and just ask you to let him die. So when I went to pick up the fresh frozen plasma, I inserted 20 mil equivalents [of potassium chloride] and they hung it and he arrested, but he did not die.” Nurse Thomas had left the room and when Rachals saw Bentley’s “QRS started widening,” she notified Dr. Calhoun and assisted in stabilizing Bentley. Dr. Calhoun testified that while he was present Bentley exhibited “a very bizzare unusual set of things ... a very spectacular, sudden set of irregular heartbeats and rapidly went into . . . cessation of heart function. . . .” Nurse Rachals called Dr. Calhoun’s attention to Bentley’s EKG widening, “which is indicative of potassium intoxication.” The medical team was successful in resuscitating Bentley.
We find this evidence sufficient to authorize a rational trier of fact to find Rachals guilty of aggravated assault beyond a reasonable doubt. Jackson v. Virginia, 443 U. S. 307 (99 SC 2781, 61 LE2d 560) (1979).
5. Rachals’ remaining enumerations of error are without merit.
Judgment affirmed.
McMurray, P. J., Banke, P. J., and Ben-ham, J., concur. Beasley, J., concurs in the judgment only. Birdsong, C. J., Carley, Sognier and Pope, JJ., dissent.