How do you solve the following problem: On rainy days, Joe is late to work with

Question

How do you solve the following problem: On rainy days, Joe is late to work with probability 0.3. Onnonrainy days he is late with probability of 0.1. With probabilityof 0.7, it will rain tomorrow: a) Find the prob. that Joe is early tomorrow b) Given that Joe was early, what is the conditional prob.that it rained? How do you solve the following problem: On rainy days, Joe is late to work with probability 0.3. Onnonrainy days he is late with probability of 0.1. With probabilityof 0.7, it will rain tomorrow: a) Find the prob. that Joe is early tomorrow b) Given that Joe was early, what is the conditional prob.that it rained?

Explanation / Answer

Given P(L/R)=.3 Therefore P(L'/R)=.7 Given P(L/R')=.1 Therefore P(L'/R')=.9 Given P(R)=.7 Therefore P(R')=.3 a)P(L')=P(L'nR)+P(L'nR') =P(L'/R)P(R)+P(L'/R')P(R') =(.7)(.7)+(.9)(.3)=.76 b)P(R/L')=P(L'/R)P(R)/P(L') (.7)((.7)/.76=.645

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