Probability

Probability

1. Definitions

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

2. Value

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

3. Experimental Probablity

   • What actually happens is an experiment P(E)= Number of outcome favourable to E/ Number of all possible outcomes of the experiment.

4. Theoretical Probability

   • 0 < P(E) < 1 What we expect to happen in an experiment P(E) =Number of trials in which the event happened/ Total number of trials

5. Examples

   • Dice
     • Two dice are rolled, what is probability of getting 12 a sum? SOLUTION: Number of possible outcomes =36 Number of favourable outcomes= 1 i.e. (6,6) P(E)= 1/36
   • Card
     • 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 Prob. P(E) = 1/2
   • Coin
     • What is the probability of getting an ace from a pack of 52 cards? SOLUTION: Number of favourable outcomes= 1 Number of possible outcomes= 52 P(E)= 4/52= 1/13