The possibility and probability of natural transfer of viable microbes from Mars to Earth and Earth to Mars traveling in meteoroids during the first 0.5 Ga and the following 4 Ga are investigated, including: --radiation protection against the galactic cosmic ray nuclei and the solar rays, dose rates as a function of the meteorite's radial column mass (radius x density), combined with dose rates generated by natural radioactivity within the meteorite; and survival curves for some bacterial species using NASA's HZETRN transport code --other factors affecting microbe survival: vacuum; central meteorite temperatures at launch, orbiting, and arrival; pressure and acceleration at launch; spontaneous DNA decay; metal ion migration --mean sizes and numbers of unshocked meteorites ejected and percentage falling on Earth, using current semiempirical results --viable flight times for the microbe species Bacillus subtilis and Deinococcus radiodurans R1 --the approximate fraction of microbes (with properties like the two species studied) viably arriving on Earth out of those ejected from Mars during the period 4 Ga BP to the present time, and during the 700 Ma from 4.5 to 3.8 Ga. Similarly, from Earth to Mars. The conclusion is that if microbes existed or exist on Mars, viable transfer to Earth is not only possible but also highly probable, due to microbes' impressive resistance to the dangers of space transfer and to the dense traffic of billions of martian meteorites which have fallen on Earth since the dawn of our planetary system. Earth-to-Mars transfer is also possible but at a much lower frequency.