Question 123456

1. For the events A and B, P(A) = 0.6, P(B) = 0.8 and P(A U B) = 1. a) Find P(A n B) b) Find P(A' U B') c) Find P(A'n B') 2. For events A and B, P(A)=0.6, P(B)= 0.7 and P((B|A) = 0.2. a) Find P(An B) b) Find P((A|B) 3. The events A and B are independent such that P(A) =0.4 and P(A U B)= 0.88. Find P(B) 4. The events A and B are such that P(B | 4)= 0.2, P(B|4') = 0.3, P(A|B)= 0.4 and P(A) = p. a) Find the value of p. b) Are A and B independent? 5. The probability that a girl chosen at random is a left-hander is = Calculate the probability that among a group of ten girls chosen at random a) None is left-hander b) Exactly one is left-hander c) Among 100 groups of ten girls, how many groups would you expect to obtain more than one girl are left-hander. 6. In the packing of chicken egg, it is found that 5% of the eggs crack in the process. The same grade of eggs is selected at random and packed in boxes of 6. If a box is selected, calculate that there will be a) Exactly one crack egg b) No crack egg c) If 200 boxes are selected, estimate the mean of boxes which contain no crack egg