24 Controlling the water hyacinth. Entomologists are continually searching for new biological agents to control the water hyacinth, one of the world’s worst aquatic weeds.

An insect that naturally feeds on the water hyacinth is the delphacid. Female delphacids lay anywhere from one to four eggs onto a water hyacinth blade. The Annals of the Entomological Society of America (Jan. 2005) published a study of the life cycle of a South American delphacid species. The following table gives the percentages of water hyacinth blades that have one, two, three, and four delphacid eggs:

a. One of the water hyacinth blades in the study is randomly selected, and x , the number of delphacid eggs on the blade, is observed. Give the probability distribution of x .

b. What is the probability that the blade has at least three delphacid eggs?

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One Two Three Four Egg Eggs Eggs Eggs Percentage of Blades 40 54 2 4 Source: Sosa, A. J., et al. "Life history of Megamelus scutellaris with description of immature stages." Annals of the Entomological Society of America, Vol. 98, No. 1, Jan. 2005 (adapted from Table 1).