PROBABILITY

PROBABILITY

1. Theoretical Probability

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

2. Experimental Probability

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