Answer to Question #187013 in Statistics and Probability for Chairmane

Question #187013

 From a box of a dozen rocket-propelled grenade (RPG), 4 are selected at random and fired. If the box contains 3 defective RPG’s, what is the probability that (a) all 4 will fire? (b) at most 2 will not fire? 


1
Expert's answer
2021-05-02T17:52:08-0400

p - RPG fire, q - RPG doesn't fire

a)

"P(p=4)=\\frac{9}{12}\\cdot\\frac{8}{11}\\cdot\\frac{7}{10}\\cdot\\frac{6}{9}=\\frac{7\\cdot2}{11\\cdot5}=\\frac{14}{55}"


b)

"P(q\\le2)=P(q=0)+P(q=1)+P(q=2)="

"=\\frac{3}{12}\\cdot\\frac{9}{11}\\cdot\\frac{8}{10}\\cdot\\frac{7}{9}+\\frac{3}{12}\\cdot\\frac{2}{11}\\cdot\\frac{9}{10}\\cdot\\frac{8}{9}=\\frac{7}{55}+\\frac{2}{55}=\\frac{9}{55}"


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