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The present paper is devoted to modelling of a probability measure of logicalconnectives on a quantum logic (QL), via a $G$-map, which is a special map onit. We follow the work in which the probability of logical conjunction,disjunction and symmetric difference and their negations for non-compatiblepropositions are studied.  We study such a $ G $-map on quantum logics, which is a probability measureof a projection and show, that unlike classical (Boolean) logic, probabilitymeasure of projections on a quantum logic are not necessarilly pureprojections.  We compare properties of a $G$-map on QLs with properties of a probabilitymeasure related to logical connectives on a Boolean algebra.

Probability Measures and projections on Quantum Logics