PROBABILITY

PROBABILITY

1. VALUE

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

2. THEORETICAL PROBABILITY

   • 0<P(E) <1 P(E)= Number of trials in which the event happened/Total no. of trials.

3. EXPERIMENTAL PROBABILITY

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

4. EXAMPLES

   • Dice : Two dice are rolled, what is the probability of getting 12 as a sum? Solution:No. of possible outcomes=36 No. of favourable outcomes=1 i.e. (6,6) P(E)=1/36
   • 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
   • 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 Probability P(E) = 1/2

5. DEFINITIONS

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