An island has three species of bird. species 1 accounts for 45% of the birds, of which 10% have been tagged. species 2 accounts for 38% of the birds, of which 15% have been tagged. species 3 accounts for 17% of the birds, of which 50% have been tagged. if a tagged bird is observed, what are the probabilities that it is of species 1, of species 2, and of species 3?

Species 1 = 24.1% Species 2 = 30.5% Species 3 = 45.5% Note: Numbers do not add to exactly 100% due to rounding. First, determine the relative population of tagged birds. Species 1 is 45% of the population, of which 10% have been tagged tagged 1 = 0.45 * 0.10 = 0.045 Species 2 is 38% of the population, of which 15% have been tagged tagged 2 = 0.38 * 0.15 = 0.057 Species 3 is 17% of the population, of which 50% have been tagged tagged 3 = 0.17 * 0.50 = 0.085 Now add up the percentages of all the tagged birds. 0.045 + 0.057 + 0.085 = 0.187 Now divide the percentage of each species tagged by the total population tagged. Species 1 = 0.045 / 0.187 = 0.241 = 24.1% Species 2 = 0.057 / 0.187 = 0.305 = 30.5% Species 3 = 0.085 / 0.187 = 0.455 = 45.5%