Sets, Relations and Functions
Combinatorics and Mathematical Induction
Binomial Theorem, Sequences and Series
Two Dimensional Analytical Geometry
Matrices and Determinants
Differential Calculus - Limits and Continuity
Differential Calculus - Differentiability and Methods of Differentiation
Introduction to Probability Theory
- Basic concepts of Probability
- Independent and Dependent events
- Conditional Probability
- Baye’s Theorem
- Axiomatic approach to Probability
An unbiased die is thrown twice. Let the event A be the odd number on the first throw and B the event odd number on the second throw. Check whether A and B events are independent.
Probability of solving specific problem independently by A and B are `1/2` and `1/3` respectively. If both try to solve the problem independently, find the probability that the problem is
- exactly one of them solves the problem
Suppose one person is selected at random from a group of 100 persons are given in the following
What is the probability that the man selected is a Psychologist?
Two urns contain the set of balls as given in the following table
One ball is drawn from each urn and find the probability that
- both balls are red
- both balls are of the same colour.
Bag I contains 3 Red and 4 Black balls while another Bag II contains 5 Red and 6 Black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag I.
The first of three urns contains 7 White and 10 Black balls, the second contains 5 White and 12 Black balls and the third contains 17 White balls and no Black ball. A person chooses an urn at random and draws a ball from it. And the ball is found to be White. Find the probabilities that the ball comes from
- the first urn
- the second urn
- the third urn
Three boxes B1, B2, B3 contain lamp bulbs some of which are defective. The defective proportions in box B1, box B2 and box B3 are respectively `1/2`, `1/8` and `3/4`. A box is selected at random and a bulb drawn from it. If the selected bulb is found to be defective, what is the probability that box B1 was selected?