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probability

Maths Class- 10th

vaneetbhanot
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probability

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  1. PROBABILITY The theory of probabilities and the theory of errors now constitute a formidable body of great mathematical interest and of great practical importance. _ R.S. Woodward

  2. The theoretical probability of an event E, written as P(E), is defined as P(E) = Number of outcomes favourable to E Number of all possible outcomes of experiment Example 1 : Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail. Solution : P(E) = Number of outcomes favourable Number of all possible outcomes of experiment Number of outcomes favourable is 1. P(E) = P(Head) = 1/2 P(tail) = ½ ( Why)

  3. For an event E, P(not E ) = 1- P(E) These are complementary events. • Example 2 : If P(E) = 0.05, what is the probability of ‘not E’? Solutions : P(E) = 1- P(E) P(E)= 1- 0.05 P(E)= 0.95 Key Note : - Sum of the probabilities of all the elementary events of an experiment is 1 and Probability of an event which is impossible to occur is 0.

  4. Complete the following statements : • Probability of an event + probability of the event ‘not E’ 1 • The probability of an event that is certain to happen is 1 • The probability of an event is greater than or equal to 0 and less than or equal to 1 • Event whose probability is certain to happen is Sure event. • Event that cannot happen is impossible event . • The probability of an event E is a number P(E) such that 0≤P(E)≤1

  5. Sample space when two dices are thrown simultaneously :- 1 2 3 4 5 6 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

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