{"id":9640,"date":"2023-06-01T15:33:47","date_gmt":"2023-06-01T10:03:47","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=9640"},"modified":"2023-06-02T17:38:27","modified_gmt":"2023-06-02T12:08:27","slug":"ap-ssc-10th-class-maths-notes-chapter-13","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-ssc-10th-class-maths-notes-chapter-13\/","title":{"rendered":"AP SSC 10th Class Maths Notes Chapter 13 Probability"},"content":{"rendered":"

Students can go through AP SSC 10th Class Maths Notes<\/a> Chapter 13 Probability to understand and remember the concepts easily.<\/p>\n

AP State Syllabus SSC 10th Class Maths Notes Chapter 13 Probability<\/h2>\n

\u2192 Theory of probability has its origin date back to 16th century.<\/p>\n

\u2192 J. Cardan, an Italian physician and mathematician wrote the first book on probability named “The Book of Games of Chance\u201d.<\/p>\n

\"AP<\/p>\n

\u2192 James Bernoulli (1654 – 1705), A.De Moivre (1667 – 1754) and Pierre Simon Laplace (1749 – 1827) made significant contribution to the theory of probability.<\/p>\n

\u2192 Experimental or empirical probability : The probability estimated on the basis of results of an actual experiment is called experimental probability of empirical probability.
\nEg : 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.<\/p>\n

Thus experimental probability = \\(\\frac{\\text { No. of trials in which the event happened }}{\\text { Total no. of trials }}\\)<\/p>\n

\u2192 Classical or Theoretical probability: Classical probability of an event (E) is defined Number as<\/p>\n

P(E) = \\(\\frac{\\text { Number of outcomes favourable to E }}{\\text { No. of all possible outcomes of the experiment }}\\)<\/p>\n

This definition was given by \u2018Pierre Simon Laplace\u2019.
\nEg: 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>\n

\u2234 P(E) = \\(\\frac{\\text { No. of favourable outcomes }}{\\text { Total events }}\\) = \\(\\frac{1}{2}\\)<\/p>\n

Note: If an experiment is conducted for many number of times, then the experimental probability may become closer and closer to theoretical probability.
\n\"AP<\/p>\n

\"AP<\/p>\n

\u2192 The probability of a sure event is 1.<\/p>\n

\u2192 The probability of an impossible event is zero.<\/p>\n

\u2192 The probability of an event E is a number P(E) such that 0 \u2264 P(E) \u2264 1.<\/p>\n

\u2192 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.<\/p>\n

\u2192 For any event E, P(E) + P(\\(\\overline{\\mathrm{E}}\\)) = 1, where E and \\(\\overline{\\mathrm{E}}\\) are complementary events.<\/p>\n

\u2192 Playing cards and their probability : A deck of playing cards consists of 52 cards which are divided into four suits of 13 cards each.
\nThey are:
\n\"AP<\/p>\n

\u2192 The cards in each suit are:
\n\"AP
\nEg : When a card is drawn at random from a deck of cards then<\/p>\n