Sedimentary rocks are a mixture of minerals and pores. Engineers employ well (or borehole) logging to make a detailed record of the mineral composition of the rock penetrated by a borehole. One important measure is shale density of a rock (measured as a fraction between 0 and 1). In the journal SPE Reservoir Evaluation & Testing (Dec., 2009), petroleum engineers modeled the shale density with the beta distribution. Assume shale density, Y, follows a beta distribution with α = 3 and β = 2. Find the probability that the shale density of a rock is less than .5.