P( HH) U P( TT) = P( HH) + P( TT) = ¼ + 9 / 28 = 16 / 28 = 4 / 7 P( E) where, E = One head. P( HT) U P( TH) = P( HT) + P( TH) = 1 / 7 + 2 / 7 = 3 / 7 P( E) where, E = Both Tail P( TT) = 9 / 28
Probabilities of equally likely outcome: Let P( ωi) = p, for all ωi ∈ S where 0 ≤ p ≤ 1, then p = 1 / n where n = number of elements.
Probability of the event‘ A or B’ P( A∪B) = P( A) + P( B) − P( A∩ B) Probability of the event‘ A and B’ P( A∩B) = P( A) + P( B) − P( AU B) Probability of the event‘ Not A’ P( A ′) = P( not A) = 1 – P( A)
Numerical: A bag contains 9 similar discs of which 4 are red, 3 are blue and 2 are green.. A disc is drawn at random from the bag. Calculate the probability that it will be( i) red,( ii) green,( iii) blue,( iv) not blue,( v) either red or blue
Solution: Total number of disc is 9