### Chapter at a Glance

**1. Conditional Probability **– Let E and F be two events of a random experiment, then the probability of occurrence of E under the condition that F has already

**2. Multiplication Theorem on Probability** – Let E and F be two events associated

**3. Independent Event–**

**4. Theorem of total Probability **– Let {E1, E2, ……., En}. be a partition of sample

**5. Baye’s Theorem **– If E1, E2, …., En are mutually exclusive and exhaustive

**6. Probability Distribution of a Random Variable **– Let real numbers x1, x2, …..,xn be the possible value of random variable X and p1, p2……, pn be probability

**7. Mean or Expectation of a Random Variable** – Let X be a random variable

**8. Variance and Standard Deviation of a Random Variable **– Let X be a random variable whose possible values x1, x2, ……, xn occur with probabilities p(x1),

**9. Bernoulli Trials –**Trials of a random experiment are called Bernoulli trials, if they satisfty the following conditions:

- There should be a finite number of trials
- The trials should be independent
- Each trial has exactly two outcomes: success or failure
- The probability of success remains the same in each trial.

In a Bernoulli trial, probability of success is denoted by p and probability of failure is denoted by q and p + q = 1 i.e., p = 1 – q and q = 1 – p

1**0. Binomial Distribution** – Probability distribution of number of successes, in an experiment consisting of n Bernoulli trials are obtained by Binomial expansion of (q + p)n. Such a probability distribution is

**11. Probability function – **The probability of x success in a Binomial trials is denoted by p (X = x) or P(x) and is given by