a. In 2019, UNZA management sent delegates to an Annual Economic Summit held in Livingstone. 20 delegates were from the school of education and 40 delegates from the school of humanities. A random sample of 10 UNZA delegates at the summit was asked to fill out attendance sheets. What is the probability that;

i. None of them in the sample is a delegate from school of education?

ii. Only one of them in the sample is a delegate from school of education?

iii. Exactly nine delegates in the sample were from the school of humanities?

iv. The sample had at least two delegates from the school of education?

b.

i. Assume the events A and B are independent. Show that the events A and B are independent.

ii. Use your knowledge of set theory to answer the following:

a. Let's assume A, B and C are independent events and that P (A) = 0.3333,

P (B) = 0.4 and P(C) = 0.75. Find P (AU (BC)) and P (AB).

b. Find P(A) given that P(AB) = 0.7 and P(AB) = 0.9