Revision Notes: Probability | Mathematics Class 10 ICSE PDF Download

Important Concepts

• Probability is a concept which numerically measures a degree of uncertainty and therefore of certainty of the occurrence of events.
• An action which results in one of several outcomes is called an experiment.
• An experiment is called random if it has more than one possible outcome and cannot be predicted or determined in advance. i.e. Tossing a coin, Rolling a die.
• The set of possible outcomes or the totality of all possible outcomes of an experiment constitutes the sample space.
• An outcome of a random experiment is called an event.
• The outcomes in an experiment which are favourable to an event which we are interested are called favourable out comes and all other outcomes are known as unfavourable outcomes.
• The sum of the favourable and unfavourable outcomes is equal to the exhaustive number of events in experiment.
• If there is no reason for any one outcome to occur is preference to any other outcome then we can say that the outcomes are equally likely.
• 4 aces, 4 queens, 4 kings, and 4 jacks are called face cards.

Measurement of Probability

• Probability of an Event = (number of outcomes favourable to event)/(number of all possible outcomes of the experiment)
  ⇒ P(E) = n(E)/n(S)
• When the probability is based on an actual experiment, it is called an empirical probability
• When a repetition of an experiment can be avoided for calculating the exact probability, the probability so obtained is called classical or theoretical probability.
• In theoretical probability, the outcomes are equally likely.
• For any event E, the event of non-occurrence of E is called its complementary event and is denoted by E.
• E and  are called complementary events.
• The sum of probabilities of an event and its complementary event is always 1.
• Impossible event: If the probability of an event = 0, the event is called an impossible event.
• Sure event: If the probability of an event = 1, the event is called a certain event or a sure event.
• Probability of any event can never be less than 0 or more than 1.

Important concepts

• Tossing of two coins simultaneously or tossing one coin twice, gives the same outcomes.
• In a coins is tossed n times or n coins are tossed simultaneously, the number of possible outcomes = 2ⁿ.
• Rolling a dice two times gives the same result as rolling two dice simultaneously.
• If a dice is rolled n times or n-dice are rolled simultaneously, the number or outcomes = 6ⁿ .