Probability Worksheet Yr Maths B Term A die is rolled. What is the probability that the number is an odd number or a? P(odd ) Pr(odd or a + 6 6 6 A set of cards is numbered {,, 6}. A card is selected at random. Find: (a) P(multiple of 5 or a multiple of 6) (a) P(multiple of 5 6) Pr(multiple of 5 or 6) + 6 5 6 (b) P(a number less than 7 or greater than 8). (b) P(< 7 > 8) 6 + 8 6 6 7 8 A card is selected at random from a pack of playing cards. Find: (a) Pa ( heart or a black card ) (b) Pan ( ace or a picture card (J,Q,K). ) + 6 (a) P(heart black) 9 Pr(heart or black) + (b) P(ace picture) 6 Pr(ace or royal)
A card is selected at random from a pack of playing cards. Find: (a) Pa ( diamond or a red card ) (b) Pa ( queen or a black card. ) (a) Pdiamond ( red card) P(diamond) + P(red card) P(red card diamond) 6 + 6 (b) Pqueen ( black card) P(queen) + P(black card) P(queen black) 6 + 8 7 5 Two fair coins are tossed. Draw a tree diagram and find the probability of tossing: (a) Heads (a) P( Heads) (b) a Head and a Tail. (b) P(Head Tail) P(HT) + P(TH) Pr(Head and a T + Pr(Head and a )
6 A coin is tossed and a die is rolled. (a) Draw a two-way table to show the sample space. (a) Coin outcomes Die outcomes 5 6 H (H, ) (H, ) (H, ) (H, ) (H, 5) (H, 6) T (T, ) (T, ) (T, ) (T, ) (T, 5) (T, 6) (b) Find the probability of getting a Tail with a number greater than. (b) P(Tail > ) P(5, T) + P(6, T) Pr(Tail and n ) Pr(Tail and n ) 6 7 Two dice are rolled. Use a tree diagram to find the probability of rolling: (a) two sixes (a) P(two sixes) P(SS) Pr(two sixes) 6 (b) one six (b) P(one six) P(SS ) + P(S S) Pr(one six) 6 5 + 6 5 Pr(one six) 8 5 (c) at least one six. (c) P(at least one six) P(no sixes) P(S S ) 5 6 6
8 A -digit number is to be formed using the digits, and. If the same number can be used twice, find the probability that the number formed is: (a) (a) P() 9 (b) greater than 0 (b) P(>0) P() + P() + P() Pr(>0) 9 + 9 + 9 Pr(>0) (c) odd. (c) P(odd) P() + P() + P() + P() + P() + P() 9 + 9 + 9 + 9 + 9 + 9 9 Repeat question 8 if the same digit cannot be used twice. (a) P() 6 (b) P(>0) P() + P() Pr(>0) 6 + 6 Pr(>0) (c) P(odd) P() + P() + P() + P() Pr(odd) 6 + 6 + 6 + 6 Pr(odd)
0 A coin is tossed and a die is rolled. What is the probability of an even number on the die and Tails on the coin? P(even Tails) P(even) P(Tails) 6 Pr(even and a T) An 8-sided die and a -sided die are rolled. Find: (a) P(total of 7) (b) P(total is a multiple of ). (a) P(total of 7) P(6, ) + P(5, ) + P(, ) + P(, ) + + + 8 8 8 8 + + + 8 (b) P(total is a multiple of ) P(total ) + P(total 6) + P(total 9) + P(total ) P(, ) + P(, ) + P(, 5) + P(, ) + P(, ) + P(, ) + P(, 8) + P(, 7) + P(, 6) + P(, 5) + P(, 8) 8 A netball player can shoot a goal 6 times out of every 0 throws. What is the probability of her shooting goals from the next throws? P( goals) 0 6 0 6 9 Pr ( goals) 5
A bag contains 0 apples of which are rotten. Two apples are selected. What is the probability of selecting: (a) bad apples? (b) good and bad apple? (a) P( bad apples) 0 9 Pr ( bad apples) 5 (b) P ( good apple and bad apple ) P(good and bad) + P(bad and good) 6 6 + 0 9 0 9 0 0 + 870 870 0 5 Annette is late for work once every 0 days. Glenda her assistant is late for work once every 5 days. What is the probability that: (a) they are both on time? (b) only one of them is on time? (a) P(both on time) 0 9 5 8 Pr (both on time) 5 (b) P(one on time) P(Annette on time and Glenda late) + P(Annette late and Glenda on time) 9 + 0 5 0 5 50
5 A gambling game requires the gambler to correctly match balls drawn from a barrel containing 99 numbered balls. What is the probability the gambler correctly matches: (a) both balls? (b) one of the balls? (a) P(both balls) 99 98 Pr (both balls) 85 (b) P(one of the balls) P(first ball and not the second) + P(second ball and not the first) 97 97 + 99 98 99 98 9 9 + 970 970 9 85 6 Campbell has a 0.6 chance of passing a spelling test and a 0.8 chance of passing a numeracy test. (a) Find the probability that Campbell passes both his tests. (a) P(S N) 0.6 0.8 0.8 (b) Find the probability that Campbell passes only one test. (b) P(passes only one test) P(S, not N) + P(not S, N) (0.6 0.) + (0. 0.8) 0. + 0. 0. 7 In her drawer, Mai has 6 blue socks and red socks. Mai randomly selects socks. What is the probability of Mai selecting socks with the same colour? P(same colour) P( blue socks) + P( red socks) 6 5 + 0 9 0 9 0 + 90 90 7 5
8 Two cards are randomly selected from a pack of cards. What is the probability both cards are: (a) black? 6 5 (a) P(both black) 5 5 0 (b) clubs? (b) P(both clubs) 5 7 (c) aces? (c) P(both aces) 5 Pr (both ace (d) black aces? (d) P(both black aces) 5 6 (e) A black card followed by a red card (f) A black and red card 9 In a class of 8 students, students are selected at random. Mark and Elise are two students in this class. What is the probability that: (a) one of them is selected? (b) both are selected? (e) P(black and Red) 6 6 5 5 (f) P(black and red) P(!!) or P(!!) 6 6 5 6 5 + 6 6 5 (a) P(one is selected) P(Mark selected and Elise not) + P(Elise not and Mark selected) + P(Elise selected and Mark not) + P(Mark not and Elise selected) 8 7 5 78 6 7 + 8 7 + 8 7 (b) P(both are selected) 8 7 6 + 7 8 7 Pr(both are selected 78