(15 points) A study was conducted to determine if a medicine helps to shorten the length of a cold. 200 subjects were recruited who had suffered from a cold and either took the medicine or not. The length of times in days the subject suffered from the cold was noted. The following table contains the results. Medicine? Cold Length Yes No 1-3 Days 86 19 4-7 Days 16 79

a. (5 points) If a subject is chosen at random, what is the probability the subject both took the medicine and had the cold for 1-3 days?

b. (5 points) If a subject is chosen at random, what is the probability the subject took the medicine given that the subject's cold lasted for 1-3 days?

c. Are the events 'subject took the medicine' and 'cold lasted for 1-3 days' independent or dependent? Why or why not?