Mathilde drives home from work every day. If there is no traffic jam, she can ma
ID: 3256603 • Letter: M
Question
Mathilde drives home from work every day. If there is no traffic jam, she can make it home in fewer than 20 minutes, however if there is a traffic jam it will take here at least 35 minutes. In her area, if it is sunny then there will be a traffic jam 30% of the time, if it is raining then there will be a traffic jam 50% of the time, and if it is snowing then there will be a traffic jam 80% of the time. Where she lives, the weather is always rainy, snowing, or sunny. i) Tomorrow the forecast is for 20% chance of rain and 5% chance of snow. What is the probability that if she leaves work at 5: 00 pm she will be home before 5: 20 pm? ii) Unfortunately, she doesn't get home until 5: 40. What was the probability that it actually rained that day? That it actually snowed?Explanation / Answer
i)she will be home before 5:20 pm means there should be no traffic Jam
probability =sunny and no traffic Jam+raining and no traffic jam+snow and no traffic Jam
=(1-0.2-0.05)*(1-0.3)+0.2*(1-0.5)+0.05*(1-0.8)=0.635
(ii) probabilty that she would not get home untill 5:40 =probabilty of traffic Jam
=sunny and traffic Jam+raining and traffic jam+snow and traffic Jam
=(1-0.2-0.05)*0.3+0.2*0.5+0.05*0.8=0.365
hence probabilty of rain given would not get home =0.2*0.5/0.365=0.2740
probabilty of snow given would not get home =0.05*0.8/0.365=0.1096