Formula Sheet – Probability – Class X

1. The science which measures the degree of uncertainty is called probability.

2. There are two types of approaches to the study of probability. These are experimental or empirical approach and theoretical approach.

3. In the experimental approach to probability, we find the probability of the occurrence of an event by actually performing the experiment a number of times and record the happening of an event.

4. In the theoretical approach to probability, we predict the results without actually performing the experiment.

5. The observations of an experiment are called its outcomes.

6. An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance, is called a random experiment.

7. The word unbiased means each outcome is equally likely to occur. For example, an unbiased die indicates that each of the outcomes 1, 2, 3, 4, 5 or 6 has equal chances to occur. Throughout this chapter, we shall assume that all the experiments have equally likely outcomes.

8. The theoretical probability of an event E, written as P(E) is defined as
\mathrm{P(E)=\dfrac{\text{Number of outcomes favourable to E}}{\text{Total number of all possible outcomes of the experiment}} }

9. An event having only one outcome of the experiment is called an elementary event.

10. The sum of the probabilities of all the elementary events of an experiment is 1.
In general for any event E
\mathrm{P(E)=1-P\ (not\ E)=1-P(\bar E)}
or \mathrm{P(\bar E)=1-P\ (E)}
or \mathrm{P(E)+P\ (\bar E)} =1
Here the event \bar E , representing not E, is called the compliment of the event E.

11. The probability of the event which is impossible to occur is 0. Such an event is called an impossible event.

12. The probability of an event which is sure (or certain) to occur is 1. Such an event is called a sure or a certain event.

13. For an event E, we have 0 < P(E) < 1.

14. A die is a well balanced cube with its six faces marked with numbers or dots 1 to 6. When we throw a die we are interested in the number that occurs on the top face.

15. The pack or deck of playing cards consists of 52 cards, 26 of red colour and 26 of black colour. There are four suits each of 13 cards namely hearts , spades , diamonds and clubs. Each suit contains ace, king, queen, jack or knave, 10, 9, 8, 7, 6, 5, 4, 3, 2.
There are 4 aces, 4 kings, 4 queens, 4 jacks, 4 tens, and so on in a pack. Kings, queens, and jacks are called face cards.

Scroll to Top