Probability

Probability

1. Definition

   • Elementary event
     • Event having only one outcome of the experiment
   • Sure or certain event
     • When event having probability to occur as 1
   • Complementary event
     • For event E, complementary P(E)' =1-P(E)

2. Examples

   • Dice
     • Two dice are rolled, what is probability of getting 12 as a sum? Solution: No. of possible outcomes =62 = 36 No. of favourable outcomes = 1 i.e. (6, 6) P(E) = 1/36
   • Coin
     • When a coin is tossed, what would be the probability of appearing head? Solution: Total outcomes = 2 i.e. (H,T) Favourable outcomes= 1 Required probability P (E) = 1/2
   • Card
     • What is the probability of getting an ace from a pack of 52 cards? Solution: No. of favourable outcomes= 4 No. of possible outcomes= 52 P (E) = 4/52 = 1/13

3. Theoretical Probability

   • 0 ≤ P(E) ≤ 1
     • P(E)= No. trials in which the events happened / Total no. of trials
     • what we expect to happen in an event

4. Experimental Probability

   • What actually happens in an event
     • P(E) = No. of outcomes favourable to E / No. of all possible outcomes

5. Value

   • Sum of the probabilities of all elementary events is 1
     • For events A,B,C; P(A) + P(B) + P(C) = 1