We re-examine the classic problem of risk aversion and self-protection in this paper. In the beginning of this paper, we conduct comparative statics of risk aversion and prevention efforts based on the mono-periodic two states model of choice under risk. We show this new condition is effective with self-insurance-cum-protection model (Lee, 1998), in which the decision maker's activities to prevent the risk can sever both as self-insurance and self-protection. We suggest a new condition that increased risk aversion induces more prevention activities. This new condition requires only one assumption concerning fear of ruin coefficient, marginal effect of SICP activity on probability and marginal cost of SICP activity. By applying interval dominance order (Quah and Strulovici,2009), we find that a decision maker will exert higher level of SICP activity if he becomes more risk averse, under the condition that his hazard rate is higher than the 'boldness' coefficient (Aumann and Kurz,1977). This new condition is effective even when the optimal level for SICP activity is not interior solution. With our method, the assumption, that optimal solution is interior, is not necessary and marginal utility functions do not need to be monotonic on the interval [0, w0]. Based on this, the optimal solution can be corner solution or inflection point solution. And the DM's attitude towards risk can be variable. Hence, the relation suggested by our findings is more consistent with real world situations.