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A survey found that 10% of Americans believe that hey have seen a UFO. For a sample of 10 people, find each probability:

a. That at least 2 people believe that they have seen a UFO

b. That 2 or 3 people believe that they have seen a UFO

c. That exactly 1 person believes that he or she has seen a UFO

Guest Feb 17, 2020

CubeyThePenguin · Answer 1 · 2022-01-30T03:56:37

a) find the probability that 0 or 1 people have believed that they have seen a UFO, then subtract from 1.

$1 - (0.1)^{0}(0.9)^{10} - (0.1)^{1}(0.9)^{9} \approx 0.6125 = \boxed{61.25\%}$

b) $(0.1)^2(0.9)^8 + (0.1)^3(0.9)^7 \approx 0.00478 = \boxed{0.478\%}$

c) $(0.1)^1(0.9)^9 \approx 0.0387 = \boxed{3.87\%}$