Answer:
0.55
Step-by-step explanation:
There are four things you need to keep in mind,and the question is too easy to solve , so following are those four things
1)Jamal travelling by Taxi before 7 PM
It is given that Jamal uses the bus for 70 percent of the time so he will use the taxi for (100-70)%=30% of the time.
and also it is given that he arrives home by taxi after 7 PM , 15% of the time so he will arrive home by taxi before 7 PM ,(100-15)=85% of the time,
so by multiplication law of probability , the probability that Jamal will arrive by taxi before 7 PM =0.30*0.85=.255
2)Jamal travelling by Taxi after 7 PM
Similarly by considering the above situations as described in first part,
the probability that Jamal will arrive by taxi after 7 PM=0.30*0.15=.045
3) Jamal travelling by Bus before 7 PM
Now considering the case of the bus, it is given that Jamal arrives home after 7 PM 8 percent of the time. so for before 7 PM it will be 100-8= 92%
Similarly the probability that Jamal will arrive by bus before 7 PM=0.70*0.92=.644
4) Jamal travelling by Bus after 7 PM
Similarly on the basis of above explanation we can easily say that the probability that Jamal will arrive by bus after 7 PM=0.70*.08=.056
so, the probability that Jamal chose to get home from work by bus, given that he arrived home after 7 pm=