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Combination of two Events
Addition TheoremP( A U B) = P(A) + P(B)  P( A Ç B)Solved Example A box contains 36 tickets numbered 1 to 36. One ticket is drawn at random. Find the probability that the number on the ticket is either divisible by 3 or is a perfect square. Solution n(S)= 36 Let A be the event that the number is divisible by 3. A = { 3,6,9,12,15,18,21,24,27,30,33,36 } n(A) = 12 P(A) = 12/36 Let B be the event that the number on the ticket is a perfect square. P(B) = { 1,4,9,16,25,36 } n(B) = 6 P(B) = 6/36 Now A Ç B = { 9, 36} n( A Ç B )= 2 P( A Ç B ) = 2/36 The required probability is P(A U B) P(A U B) = P(A) + P(B)  P( A Ç B) = 12/36 + 6/36 2/36 = 4/9
