1. At Least One P(x)

2. P(A) = 1 – P(A) P(At Least One Event) = 1 – P(NONE event) or = 1 – P( ALL opposite ) i.e. Suppose a family has 3 children, find the probability of having at least one girl. P(A.L.O. Girl) = 1 – P(NO girls) or 1 – P(ALL BOYS)

3. P(A.L.O. Girl) = 1 – P(NO girls) or 1 – P(ALL BOYS) = 1 – [ P(B1) · P(B2) · P(B3) ] = 1 – [½ · ½ · ½ ] = 1 – 1/8 = 7/8

4. Find the probability of getting at least one correct question on a true/false test that is answered randomly. There are 4 questions on the test. P(A.L.O. Correct) = 1 – P(NONE Correct) = 1 – P (ALL WRONG) = 1 – [P(w1)·P(w2)·P(w3)·P(w4)] = 1 – [ ½ · ½ · ½ · ½ ] = 1 – 1/16 = 15/16

5. Suppose we have one deck of cards and we want to draw 2 cards (NOT replacing the 1 st ). Find the P(at least one K) P(A.L.O. K) = 1 – P(NO kings) = 1 – [ P(K1) and P(K2) ] = 1 – [ P(K1) and P(K2|K1) = 1 – [ 48 · 47 ] 52 51 = 1 – [ 12 · 47 ] 13 51 = 1 – [.851] =. 149