Probability rules worksheet NAME A 0 16 0 1 0 0 31 B 0 43 1 If P A 0 26 and P B 0 41 and P A B 0 1 find the following a P A U B 0 26 0 41 0 10 0 57 b P B A c Are A and B disjoint events Why or why not d Are A and B independent events Why or why not No P A B 0 1 0 No P B A 0 3846 P B 0 41 a P W and J P W J P W P J W 0 6 0 2 0 12 P G M 0 42 0 33 0 1386 b P W or J P W U J 0 6 0 34 0 12 0 82 3 If P W 0 6 and P J 0 34 and P J W 0 2 find the following 4 If P Y 0 45 and P L 0 60 and P Y L 0 22 find the following a P Y U L 0 45 0 60 0 22 0 83 2 If P G 0 42 P M 0 33 and G and M are independent what s the probability of G and M b P L Y d Are Y and L independent events Why or why not c Are Y and L disjoint events Why or why not No P Y L 0 22 0 No P L Y 0 4889 P L 0 60 a P T and B P T P B T 0 51 0 18 0 0918 P D U R 0 32 0 13 0 45 6 If P T 0 51 and P B 0 28 and P B T 0 18 find the following 5 If P D 0 32 P R 0 13 and D and R are disjoint what is the probability of D or R b P T or B 0 51 0 28 0 0918 0 6982 7 Suppose in a lab 24 of the mice are albino 56 are brown and the rest are grey a What is the probability that a randomly selected mouse is i Grey P G 0 20 ii Not albino P AC 0 76 iii Grey or Albino P G U A 0 44 b If the type of mouse is independent of the next what is the probability that i 2 randomly selected mice are both brown P B B 0 56 0 56 0 3136 ii 2 randomly selected mice are albino then brown P A B 0 24 0 56 0 1344 iii 2 randomly selected mice are albino and grey P A G 0 24 0 20 2 0 096 iv 2 randomly selected mice are not grey P GC GC 0 80 0 80 0 64 v At least 1 out of 4 randomly selected mice is albino P at least 1 A out of 4 1 P AC AC AC AC 1 0 76 4 0 6664 vi The first albino mouse is the 5th one selected P AC AC AC AC A 0 76 4 0 24 0 0801 8 In the parking lot of the a large mall 64 of cars are foreign made 12 are the color blue and 7 7 are blue and foreign made cars a Draw a Venn Diagram F B 563 077 043 317 b What is the probability that a randomly selected car was i A foreign car or a blue car P F U B 0 683 ii Not a foreign car and a blue car P FC B 043 iii A foreign car given it was blue P F B 0 6417 0 077 0 12 iv Not blue given it was not a foreign car c Is being a foreign car and being blue mutually exclusive independent P BC FC Not Mutually Exclusive because P F B 0 077 0 Independent because P F B P F 0 6427 0 64 9 The following table shows the breakdown of sex and degree among a university s faculty What is the probability that a randomly selected professor is a Male and has a Doctorate P Male D b Male or has a Doctorate P Male U D Is a Male given they have a Doctorate c P Male D d A female with a Masters degree e P Masters F Is sex and degree independent Disjoint Independent Yes P Male D 0 70 P M 0 6970 Disjoint No P Male D 0 4242 0