Refer to the Annals of the Entomological Society of America (Jan. 2005) study of the life cycle of a South American delphacid species, Exercise 4.3 (p. 138). Recall that entomological engineers have found that the delphacid is a natural enemy of water hyacinth. The table giving the percentages of water hyacinth blades that have one, two, three, and four delphacid eggs is reproduced here. Consider a sample of 100 water hyacinth blades selected from an environment inhabited by delphacids. Let Y₁, Y₂, Y₃, and Y₄ represent the number of blades in the sample with one egg, two eggs, three eggs, and four eggs, respectively. Find the probability that half of the sampled blades have one egg, half have two eggs, and none of the blades has three or four eggs.

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One Egg TWO Eggs Three Eggs Four Eggs Percentage of Blades 40 54 2 4