PROBABILITY

PROBABILITY

1. Theoretical Probability

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

2. Experimental Probability

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

3. Value

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

4. Definitions

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

5. Examples

   • DICE; Two dice are rolled ,what is the probability of getting 12 as a sum? SOLUTION: Number of possible outcomes = 6*6 = 36. Number 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 P(E) = 1/2.
   • CARD; What is the probability of getting an ace from a pack of 52 cards? SOLUTION: Number of favourable outcomes = 4 Number of possible outcomes = 52 P(E) = 4/52 = 1/13.