
878 S.W.2d 837 (1994)
AETNA CASUALTY AND SURETY COMPANY, Plaintiff-Appellant,
v.
Sarah BOLLIG and Faye Levin-Fine, Personal Representative of the Estate of Jack Miller, deceased, Defendants-Respondents.
No. 18958.
Missouri Court of Appeals, Southern District, Division Two.
June 24, 1994.
*838 Frank Cottey, Patricia A. Keck, Schroff, Glass & Newberry, Springfield, for plaintiff-respondent.
Paul G. Taylor, Webb City, for defendant-appellant.
PREWITT, Judge.
Plaintiff sought declaratory judgment determining that the policy of insurance it issued to Jack Miller and Linda Miller, husband and wife, did not provide liability coverage for a wrongful death action for the death of Linda Miller. That action was brought by defendant Sarah Bollig against defendant Faye Levin-Fine, as personal representative of the estate of Jack Miller, deceased. The wrongful death petition stated Jack Miller "negligently and carelessly shot and killed Linda Miller". Immediately after her death, Jack Miller shot and killed himself with the same pistol. Plaintiff appeals from a decision denying it the relief sought.[1]
Plaintiff asserts that it has no coverage because the evidence established that Jack Miller intentionally killed Linda Miller. Its insurance policy excluded from coverage acts by an insured which are "expected or intended". Following nonjury trial the trial court determined that an intentional shooting was not shown by a preponderance of the evidence as Jack Miller's "intent immediately preceding or at the discharge of the gun is unproven and whether the gun discharged accidentally, intentionally, by malfunction or otherwise is uncertain."
The dispute presented is basically factual rather than legal. The parties appearing here agree that if Jack Miller intentionally shot Linda Miller, there is no coverage. Plaintiff states in its first point that the trial court's findings and determination "are against the weight of the evidence, are erroneous, and are not supported by substantial evidence, in that the substantial and credible evidence established that the death of Linda A. Miller was expected or intended by Jack Miller" as "[t]he overwhelming weight of the evidence conclusively illustrates that Jack Miller acted intentionally in shooting his wife" in several specific particulars.
This court should set aside a judgment on the ground that it is against the weight of the evidence only when this court has a firm belief that the judgment is wrong. Goodnight v. Curry, 618 S.W.2d 278, 279 (Mo.App.1981). "Weight of the evidence" means its weight in probative value, not the quantity or amount of evidence. Id. The *839 weight of evidence is not determined by mathematics, but on its effect in inducing belief. Id. On appellate review of a case tried without a jury, "[d]ue regard shall be given to the opportunity of the trial court to have judged the credibility of witnesses." Rule 73.01(c)(2).
The burden was on plaintiff to establish that an exclusion barred coverage. American Family Mut. Ins. Co. v. Lacy, 825 S.W.2d 306, 314 (Mo.App.1991). In this civil action that burden is satisfied by a preponderance of the evidence. Fujita v. Jeffries, 714 S.W.2d 202, 206 (Mo.App.1986), states:
"Preponderance of the evidence is that which is of greater weight or more convincing than the evidence which is offered in opposition to it; that is, evidence which as a whole shows the fact to be proved to be more probable than not."
Under this exclusion, to prevent coverage plaintiff had to show that the insured intended the act causing the injury and "that injury was intended or expected from these acts." American Family Mut. Ins. v. Pacchetti, 808 S.W.2d 369, 371 (Mo. banc 1991).[2]
Whether Jack Miller intended to harm his wife can be inferred from the circumstances surrounding her death; one is presumed to intend the probable consequences of his acts. Truck Ins. Exchange v. Pickering, 642 S.W.2d 113, 116 (Mo.App. 1982). The court in Pickering stated:
"Probing one's state of mind is an elusive task at best. Supplanting an objective standard with a subjective standard for determining whether the act or conduct of an insured is `intentional' or `expected or intended' for purposes of assessing coverage would emasculate apposite policy provisions by making it impossible to preclude coverage for intentional acts or conduct absent admissions by insureds of a specific intent to harm or injure. Human nature augers against any viable expectation of such admissions."
The trial court made certain findings of fact which are not here disputed. Plaintiff contends that there are additional undisputed facts which are relevant and that the conclusion drawn by the trial court from the facts was erroneous. The facts found by the trial court are as follows, omitting the numbers preceding the paragraphs:
"That on September 12, 1990, Linda Agnes Miller and her spouse, Jack Miller, were found dead in bed at their home at 4013 Belle Locke, Joplin, Missouri.
That Linda Agnes Miller died as a result of being shot in the left temple with a .45 calibre semi-automatic pistol, and Jack Miller died as a result of being shot in the forehead with the same pistol.
That the .45 calibre pistol was found on Mr. Miller's chest with the barrel pointing to the left of his head. The hand grip of the gun was laying about the middle of his chest and his right hand laid open, palm down near his right ear. His left hand palm rested on the left side of his chest with the left index finger resting on the barrel about two inches from the end.
That there was one live round in the chamber and the gun was cocked with three live rounds in the clip. That fully loaded, the gun would hold six rounds in the clip and one in the chamber.
That during the course of the official investigation of the deaths, samples were taken from the backs of the hands of Mr. and Mrs. Miller and gunshot residue tests were performed with the results indicating that there was gun powder residue on Mr. Miller's hands and none on Mrs. Miller's hands.
That Mrs. Miller's body was to the left of Mr. Miller on the bed and a .45 calibre shell casing was found on the floor immediately adjacent to the left side of the bed and a second casing was found between the bodies on the bed.
That the .45 calibre bullets passed completely through their heads with one bullet found in the mattress and the other between a pillow and the mattress.

*840 That there was no evidence to establish when or how the pistol was loaded. In order to fire this automatic with the safety off, the trigger must be pulled while depressing the back-up safety bar.
That there was no sign of theft or forced intrusion. No bullets or blood were found in the home other than on or around the bed where the deceased were found.
That at the time of their deaths, Mr. and Mrs. Miller were the named insureds of a homeowner's insurance policy issued by Aetna Casualty And Surety Company providing personal liability coverage but excluding claims for bodily injury `which is expected or intended by any insured.'"
After finding these facts the trial court determined that an intentional act by Jack Miller "is not proven by a preponderance of the evidence. His intent immediately preceding or at the discharge of the gun is unproven and whether the gun discharged accidentally, intentionally, by malfunction or otherwise is uncertain." Judgment was entered, finding that plaintiff is obligated to defend the wrongful death action and pay any judgment entered against the estate of Jack Miller in that action.
The Jasper County Coroner testified that on both Millers there was a charred ring around the entrance wound made by the bullet caused by heat escaping from the muzzel of the gun. The coroner said this normally occurred when the barrel is in contact with the flesh. He concluded that when the gun discharged into Linda Miller's temple "it was flush, pressed against it [her temple], in contact with it." The coroner also said there was no stippling around her wound. Marks made by gun powder are called stippling. He said that in conjunction with the burn ring, there being no stippling indicates the end of the barrel was up against her flesh when fired.
The Millers' deaths were caused by a Colt.45 caliber semi-automatic United States government issue pistol. Steve Weston, a captain with the Jasper County Sheriff's Department, investigated the Millers' death. He testified that in order to fire the weapon, bullets had to be taken one at a time and inserted into the magazine. The magazine then must be inserted into the butt of the pistol. A bullet is inserted into the chamber by a manual "mechanism" on the side of the gun. The safety must be turned off and there is an additional "bar safety" that has to be depressed before the gun can be fired. Then, when the trigger is squeezed, the gun will fire and automatically reload the chamber.
Defendant acknowledges that records of Linda Miller's psychiatrist reflects that there had been marital discord, but points out that the last entries made by the psychiatrist indicate an improving relationship. A person who lived in the adjoining duplex heard an argument between the Millers on the Sunday evening before their bodies were discovered. The neighbor did not hear any gun shots.
There was a note on a table near the scene of the incident which said, "Notify Michael Talley". On top of the note was an envelope containing "a safety security box key." Defendant Bollig asserts that if, as plaintiff asserts, "the note is evidence that Jack Miller was putting his affairs in order ... it would be consistent with his suicide, but it has no more logical connection to the shooting of Linda Miller than does the evidence of suicide itself." Defendant Bollig contends that Jack Miller may have accidentally killed Linda Miller and then committed suicide "because he was distraught that he had accidentally shot his wife."
Jack Miller was in the army for 3½ years during World War II, reaching the rank of sergeant. It is logical to believe that by his military training and his ownership of the pistol he understood the use and danger of firearms. Placing a loaded pistol against Linda Miller's head, but not intending to kill her, was highly unlikely.
Obviously, in situations where the only two people present are dead, no one can ever be absolutely sure what occurred. However, absolute proof is not required. Logic and common sense indicate that on these facts it is more probable than not that Jack Miller intentionally shot Linda Miller. We have a firm belief that the judgment entered by the trial court was wrong.
*841 The judgment is reversed and the cause remanded to the trial court with directions that it set aside its judgment and enter judgment in favor of plaintiff, declaring that plaintiff has no coverage due to the death of Linda Miller, and has no obligation to defend or pay any judgment arising out of the wrongful death action.
CROW and GARRISON, JJ., concur.
NOTES
[1]  Only Defendant Bollig filed a brief in opposition to plaintiff. Defendant Levin-Fine has not appeared here.
[2]  Numerous cases involving shootings and insurance coverage are discussed and collected in Shelter Mut. Ins. Co. v. Parrish, 659 S.W.2d 315, 320-321 (Mo.App.1983). See also Steelman v. Holford, 765 S.W.2d 372 (Mo.App.1989).
