1.An examination paper has two sections namely Section A and Section B. Questions in Section A are calculation oriented, whereas questions in Section B are to be answered by writing short essays. There are six questions in Section A and eight questions in Section B. Candidates are demanded to answer any ten questions from the examination paper.

(a) How many groups of ten questions contain four from Section A and six from Section B?

(b) How many groups of ten questions contain at least one from Section A? (

c) How many groups of ten questions contain at most three from Section A?

2.Two urns: Urn-1 and Urn-2. There are 10 red balls and 25 green balls in Urn-1, whilst there are 22 red balls and 15 green balls in Urn-2. A ball is chosen as follows: Either Urn-1 or Urn-2 is chosen by tossing a loaded coin which biased at 60% to be landing tail up. If the coin lands head up, then Urn-1 is chosen, otherwise, Urn-2. Subsequently, a ball is picked at random from the chosen urn.

(a) What is the probability that the chosen ball is green?

(b) If the chosen ball is green, what is the probability that it was picked from the Urn-1?