4.112 Catching a Cold Is your chance of getting a cold influenced by the number of social contacts you have? A study by Sheldon Cohen, a psychology profes- sor at Carnegie Mellon University, seems to show that the more social relationships you have, the less sus- ceptible you are to colds. A group of 276 healthy men and women were grouped according to their number of relationships (such as parent, friend, church member, neighbour). They were then exposed to a virus that causes colds. An adaptation of the results is shown in the table:

a. If one person is selected at random from the 276 people in the study, what is the probability that the person got a cold?

b. If two people are randomly selected, what is the probability that one has four or five relationships and the other has six or more relationships?

c. If a single person is randomly selected and has a cold, what is the probability that he or she has three or fewer relationships?

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Number of Relationships Three or Fewer Four or Five Six or More Cold 49 43 34 No cold 31 57 62 Total 80 100 96