a. In baseball, hitting the ball three times out of ten times at bat is considered a very good accomplishment. (In baseball, it is written in thousandths: .300.) The last major league baseball player to hit over .400, four hits out of ten times at bat, was Ted Williams in 1941. Given the information about Williams' career, answer the questions that follow:

• total number of career hits: 2654
• total number of times at bat in his career: 7706

i.What is the probability that Ted Williams would get a hit?1 mark

ii.What are the odds in favour of Williams getting a hit?2 marks

iii.What are the odds against Williams getting a hit?1 marks

b. What is the probability given the odds are 3 : 4?2 marks

c. In a group of 100 people, 50 have cancer and 50 are cancer-free. Of the people with cancer, it is determined that 10 of them were exposed to a certain risk factor and 2 of those without cancer were also exposed.

i.What are the odds of being cancer-free if you are exposed to cancer risk factors?2 marks

ii.What are the odds of being cancer-free if you are not exposed to cancer risk factors?2 marks