Is there a chance that a mule may reproduce if bred?
It is not uncommon for female mules to come into estrus and for male mules to display signs of teasing other female equine when in estrus. Most mule owners will castrate male mules, and some will even spay female mules (remove the ovaries) in hopes of changing behavior associated with estrus or aggression. A mule is a cross between a male donkey (jack) and a female horse (mare). A hinny is the reciprocal cross, a female donkey (jenny/jennet) and a male horse (stallion). Mules have 63 chromosomes, horses have 64 chromosomes, and donkeys have 62 chromosomes. Due to the odd number of chromosomes and the fact that only 19 pairs can actually share information. Mules are believed to be sterile for a number of reasons such as the failure to produce viable oocytes and sperm cells, thus effectively blocking normal estrous cycles, sperm cell development, and fertilization.
However, there are likely more cases of mules/hinnies reproducing than we know especially in developing countries. Most recent cases of mules producing foals have been documented in Morrocco (late 1990s), China (hinny that produced a foal named Dragon in the 1980s), and most recently, a mule bred to a jack in a pasture in Colorado in 2008.
Most documented cases of mules/hinnies being fertile have been in the female mule (molly/mare mule). A majority of male mules/hinnies are castrated, but one case of a fertile hinny producing live, mature spermatozoa was documented at Texas A&M in the 1950s.
Also, mare mules have been used successfully as recipients. Colorado State University several years ago was successful in doing so. Also, keep in mind it's likely that more mules may be fertile, but we commonly do not attempt to breed mules. Mules and hinnies that have foaled in the past were bred to jacks (male donkeys).