CBSE Class 10 Mathematics Probability Notes Set 06

Basic Terms

A random experiment has several possible outcomes and its result cannot be predicted with certainty (tossing a coin, throwing a die). The collection of all outcomes is the sample space, and an event is any collection of outcomes. Outcomes are equally likely when none is favoured over another, as with a fair coin or a fair die.
One die has 6 outcomes, two dice 36, one coin 2, two coins 4 and three coins 8. A pack of 52 cards has 26 red and 26 black cards, 4 suits of 13, and 12 face cards (kings, queens, jacks).

Probability of an Event

For equally likely outcomes, \( P(E)=\frac{\text{number of outcomes favourable to }E}{\text{total number of outcomes}} \). Always \( 0\le P(E)\le1 \); an impossible event has probability 0 and a sure event has probability 1. The probabilities of all elementary events of an experiment add up to 1, and \( P(E)+P(\text{not }E)=1 \).
Take care with phrases such as 'at least', 'at most', 'neither ... nor' and 'or': list the favourable outcomes explicitly and do not count an outcome twice when two conditions overlap (for example the king of spades is both a spade and a king).

Geometric and Removal Problems

When a point or object lands at random on a region, the probability of landing in a part of it is the area of that part divided by the area of the whole region. When items are removed from a collection before drawing, reduce both the number of favourable outcomes (if the removed items were favourable) and the total number of outcomes before applying the formula.