Probability

Let U = {1, 2, 3, …., 20}. Let A, B, C be the subsets of U. Let A be the set of all numbers which are perfect squares, B be the set of all numbers which are multiples of 5 and C be the set of all numbers which are divisible by 2 and 3.

Consider the following statements:

1. A, B, C are mutually exclusive.

2. A, B, C are mutually exhaustive.

3. The number of elements in the complement set of A ∪ B is 12.

Which of the statements given above the correct?

Direction: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.

Quantity I: A bag contains 5 red, 3 black, 4 yellow, and 4 pink pens. If 4 pens are drawn at random, find the probability that 2 pens are red and 2 pens are black.

Quantity II: Find the probability such that all 4 jacks are drawn when 5 cards are drawn at random from a pack of 52 cards.

A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.

If two events are Mutually Exclusive then which of the following holds good? 

(a) Events whose occurrence do not depend on the occurrence of any other events 

(b) The occurrence of one precludes the occurrence of the other 

(c) P(A∩B)= 0 

(d) P(A ∩ B) = P(A)+ P(B)