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