This article investigates factors affecting the participation in marijuana, cocaine and heroin using micro-unit data from an Australian national survey on recreational drugs. Accounting for cross-drug correlation potentially induced by unobserved personal characteristics such as individual tastes and addictive personalities, we estimate a trivariate probit model, where the participation decisions are jointly modelled as a system with correlated error terms. The estimated correlation coefficients are significant across all three drugs. The study provides valuable empirical information on conditional and joint probabilities of drug participation. The multivariate approach is shown to provide better analysis relative to a univariate approach that does not address the endogeneity of all drug participation variables.