Grade Female Male Total
A ................... 0 ...........3 ............ 3
A- .................. 4 ...........1 ............ 5
B+ ................. 3 ...........2 ............ 5
B ................... 1 ...........4 ............ 5
B- .................. 1 .......... 2 ............ 3
C+ ................. 1 .......... 2 .............3
C ................... 4 .......... 2 .............6
C- .................. 0 .......... 1 .............1
D- .................. 0 .......... 2 .............2
Total ............ 14 .........19 .......... 33
Here is a set of follow-up questions. Using the same data, let's kick it up a notch. Please answer the following questions.
1. Are being female and achieving A- independent events? Explain why? Support your answer mathematically.
2. Are being female and achieving A- mutually exclusive events? Explain why? Prove your answer mathematically.
3. Are achieving A- and B+ mutually exclusive events? Explain why? Support your answer mathematically.
4. Are achieving A- and B+ independent events? Explain why? Support your answer mathematically.
5. Given two events are mutually exclusive, can they be independent events? Explain why? Support your answer mathematically.
6. Given two events are mutually exclusive, are they always dependent events? Explain why? Support your answer mathematically.