Woul appreciate help with this question, please. Seventy percent of the light ai

Question

Woul appreciate help with this question, please. Seventy percent of the light aircraft that disappear while inflight in a certain country are subsequently discovered. Of thosthat are discovered, 6o% have an emergency locator, while 90% ofthose not discovered do not have such a locator. a) If it has emergency locator, what is the probability thatit will not be discovered? b) If it does not have an emergency locator, what is theprobability that it will be discovered? Woul appreciate help with this question, please. Seventy percent of the light aircraft that disappear while inflight in a certain country are subsequently discovered. Of thosthat are discovered, 6o% have an emergency locator, while 90% ofthose not discovered do not have such a locator. a) If it has emergency locator, what is the probability thatit will not be discovered? b) If it does not have an emergency locator, what is theprobability that it will be discovered?

Explanation / Answer

L=has locator; L'=does not have locator; F=planefound; F'=plane not found P(F)=.7; P(F')=.3; P(L/F)=.6; P(L'/F)=.4; P(L'/F')=.9; P(L/F')=.1 Now we can find P(L)=P(F and L) + P( F' and L)=P(L/F)P(F)+P(L/F')P(F')=(.6)(.7)+.1(.3)=.45 therefore P(L')=1-.45=.55 a) Find P(F/L) P(F/L)=P(L/F)P(F)/P(L)=.6(.7)/.45=.933 b) Find P(F/L') P(F/L')=P(L'/F)P(F)/P(L')=.4(.7)/.55=.509

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