Students can go through AP SSC 10th Class Maths Notes Chapter 13 Probability to understand and remember the concepts easily.
AP State Syllabus SSC 10th Class Maths Notes Chapter 13 Probability
→ Theory of probability has its origin date back to 16th century.
→ J. Cardan, an Italian physician and mathematician wrote the first book on probability named “The Book of Games of Chance”.
→ James Bernoulli (1654 – 1705), A.De Moivre (1667 – 1754) and Pierre Simon Laplace (1749 – 1827) made significant contribution to the theory of probability.
→ Experimental or empirical probability : The probability estimated on the basis of results of an actual experiment is called experimental probability of empirical probability.
Eg : An unbiased coin is tossed for 1000 times, head turned up for 455 times and tail turned up 545 times, then the probability or likelyhood of getting a head is = \(\frac{455}{1000}\) = 0.455.
Thus experimental probability = \(\frac{\text { No. of trials in which the event happened }}{\text { Total no. of trials }}\)
→ Classical or Theoretical probability: Classical probability of an event (E) is defined Number as
P(E) = \(\frac{\text { Number of outcomes favourable to E }}{\text { No. of all possible outcomes of the experiment }}\)
This definition was given by ‘Pierre Simon Laplace’.
Eg: The probability of getting a head when a coin is tossed is given by Number of outcomes favourable to this event getting a head = 1 Number of all possible outcomes of this experiment = 2 (Head, Tail)
∴ P(E) = \(\frac{\text { No. of favourable outcomes }}{\text { Total events }}\) = \(\frac{1}{2}\)
Note: If an experiment is conducted for many number of times, then the experimental probability may become closer and closer to theoretical probability.
→ The probability of a sure event is 1.
→ The probability of an impossible event is zero.
→ The probability of an event E is a number P(E) such that 0 ≤ P(E) ≤ 1.
→ An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
→ For any event E, P(E) + P(\(\overline{\mathrm{E}}\)) = 1, where E and \(\overline{\mathrm{E}}\) are complementary events.
→ Playing cards and their probability : A deck of playing cards consists of 52 cards which are divided into four suits of 13 cards each.
They are:
→ The cards in each suit are:
Eg : When a card is drawn at random from a deck of cards then
- Getting a black or red card – equally likely exhaustive events.
- Getting an ace or king – mutually exclusive.
- Getting an ace or a hearts – not mutually exclusive since the hearts contain an ace.
→ When a coin is tossed, the outcomes are H, T (Head, Tail).
→ When a dice is thrown the outcomes are 1, 2, 3, 4, 5 and 6.
→ When two dice are thrown, the outcomes are
→ If a coin is tossed n-times or n – coins are tossed simultaneously, then the number of total outcomes = 2n.
→ If a dice is thrown for n – times or n – dice are thrown simultaneously then the number of total outcomes = 6n.