Probability
This chapter introduces the theoretical (classical) definition of probability, calculating the probability of simple events using favourable outcomes and total outcomes.
The theoretical probability of an event E, written P(E), is defined as: P(E) = (Number of outcomes favourable to E) / (Total number of possible outcomes), assuming all outcomes are equally likely.
The probability of any event lies between 0 and 1 (inclusive): 0 ≤ P(E) ≤ 1. P(E) = 0 means the event is impossible. P(E) = 1 means the event is certain. The sum of probabilities of an event and its complement is 1: P(E) + P(not E) = 1.
Q. A die is thrown once. What is the probability of getting a number greater than 4?
Total outcomes when a die is thrown = 6 (numbers 1 to 6). Numbers greater than 4 are 5 and 6, so favourable outcomes = 2. P(number greater than 4) = 2/6 = 1/3.
For a well-shuffled deck of 52 playing cards: there are 4 suits (hearts, diamonds, clubs, spades) with 13 cards each, 26 red cards and 26 black cards, 12 face cards (jack, queen, king of each suit), and 4 aces.
Q. A bag contains 3 red balls and 5 black balls. A ball is drawn at random. Find the probability that it is red.
Total balls = 3 + 5 = 8. Favourable outcomes (red balls) = 3. P(red ball) = 3/8.
The probability of an impossible event is:
Correct answer: (A) 0
Two events are called _______ if the occurrence of one prevents the occurrence of the other at the same time.
Mutually exclusive
The sum of the probabilities of all possible outcomes of a random experiment is always 1.
True — since the outcomes together cover all possibilities (the sample space), their probabilities must sum to 1.