A group of students wrote their final two examination papers, Accounting and Statistics. The results showed that 35% of the students failed Accounting and 40% of the students failed statistics. Determine the probability that a student chosen randomly from the group has:

5.1.1 Failed both papers.

5.1.2 Passed both papers.

5.1.3 Failed one paper and passed the other.

5.2 Suppose we have a sample space S={a;b; c; d;e; f; g; h; i; j } and we have events:

A= {a;b; i; d;e} ; B= {c;a;g;e;d} and C ={c;h; i; e;f}

5.2.1 Calculate the probability A C.

5.2.2 Are the events B and C mutually exclusive? Explain.

5.2.3 Draw a Venn diagram for ABC.