Interplanetary contamination - Drake-like equation
Probability that Earth microbes already exist on Mars =
time in years that bacterial life has spread over the Earth x
probability of impact large enough to produce space ejecta in any year x
probable number of meteoroids produced by impact x
probability of microbes surviving heat of Earth impact x
probability of microbes surviving in space x
probability of meteoroid headed in direction of Mars x
probability initial velocity is sufficient to reach Mars orbital distance from Sun x
probability of alignment with Mars orbital plane and Mars gravity well x
probability of microbes surviving impact with Mars
All in all, quite likely then. Should we really worry about contaminating Mars?