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The coverage problem is a fundamental problem for almost all applications in wireless sensor networks (WSNs). Many applications even impose the requirement of multilevel (<i>k</i>) coverage of the region of interest (ROI). In this paper, we consider WSNs with uncertain properties. More precisely, we consider WSNs under the probabilistic sensing model, in which the detection probability of a sensor node decays as the distance between the target and the sensor node increases. The difficulty we encountered is that there is <i>no</i> unified definition of <i>k</i>-coverage under the probabilistic sensing model. We overcome this difficulty by proposing a &#8220;reasonable&#8221; definition of <i>k</i>-coverage under such a model. We propose a sensor deployment scheme that uses less number of deployed sensor nodes while ensuring good coverage qualities so that (i) the resultant WSN is connected and (ii) the detection probability satisfies a predefined threshold <inline-formula> <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>th</mi> </msub> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>p</mi> <mi>th</mi> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>. Our scheme uses a novel &#8220;zone 1 and zone 1&#8722;2&#8221; strategy, where zone 1 and zone 2 are a sensor node&#8217;s sensing regions that have the highest and the second highest detection probability, respectively, and zone 1&#8722;2 is the union of zones 1 and 2. The experimental results demonstrate the effectiveness of our scheme.