There are 3 doors with one door having an expensive car

behind it and each of the other 2 doors having a goat behind them. Monty Hall,

being the host of the game, knows what is behind each door. A contestant is asked

to select one of the doors and he wins the item (car or goat) behind the selected

door. The contestant selects one of the doors at random, and then Monty Hall

opens one of the other two doors to reveal goat behind it (note that at least one of

the other two doors has a goat behind it and Monty Hall knows the door having

goat behind it). Monty Hall offers to trade the door that contestant has chosen for

the other door that is closed. Should the contestant switch doors if his goal is to

win the car?

The inverse of a symmetric matrix is

Suppose that 20 persons P1,..., Pn are made to stand in a row at random.

Find the probability that there are exactly 4 persons between Pl and P2. pick the closest answer

A batch of 580 students taking the course Probability and Statistics is divided into three

sections A.B.C. Section A has 180 students while Sections B and C have 200 students each.

After the examination, it is observed that 11 students from Section A scored EX grade while

7 students failed the course. In Section B. 9 students scored EX while 12 students failed the

course. In Section C, 13 students scored EX while 12 students failed the course.

If a randomly selected student from the batch has failed the course, what is the probability

that the student belongs to either Section B or Section C?  Pick the closest answer.