6.30 It has been estimated that one in five Americans suffers from allergies. Th

Question

6.30 It has been estimated that one in five Americans suffers
from allergies. The president of Maners University
plans to randomly select 10 students from the undergraduate
population of 1400 to attend a dinner at his home.
Assuming that Maners students are typical in terms of
susceptibility to allergies and that the college president’s
home happens to contain just about every common allergen
to which afflicted persons react, what is the probability
that at least 8 of the students will be able to stay for
the duration of the dinner event?

Explanation / Answer

1400*(1-1/5)=1120 1120C8 * (1400-1120)C2 / 1400C10=0.303 1120C9 * (1400-1120)C1 / 1400C10=0.2684 1120C10 * (1400-1120)C0 / 1400C10=0.1065 add up all the probability 0.303+0.2684+0.1065=0.6779

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