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EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions Edexcel Exam Style Questions 1. For the events A and B, P (A B') = 0.32 P(A' B ) = 0.11 and P(A B)= 0.65 (a) Draw a Venn diagram to illustrate the complete sample space for the events A and B. (3) (b) Write down the value of P(A) and the value of P(B). (3) (c) Find P(A B'). (2) (d) Determine whether or not A and B are independent. (3) (Total 11 marks) Worked Solution (a) A B 0.32 0.22 0.11 0.35 Hint: P ( A B ) = 0.65 means A or B or both is the sum of all the numbers in A, B (b) P(A) = 0.54 P(B) = 0.33 P ( A B¹) (c) P ( A|B¹) P (B¹) 0.32 0.67 0.478 (3 SF) Page 1 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions (d) P(A) = 0.54 P(B) = 0.33 P(A) x P(B)= 0.54 x 0.33 = 0.1782 P(A B )= 0.22 P( A B) P( A) P(B) Therefore the events A,B are not independent Page 2 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions 2. A tennis player has two matches coming up. He estimates that the probability of him winning the first match is 0.5, the probability of winning the second match is 0.3 and the probability of winning both is 0.2 (a) Find the probability that he does not win either. (3) (b) Find the probability that he wins exactly one match. (2) (c) Given that he does not win the first match, find the probability that he wins the second. (2) (d) Determine whether winning the first match and winning the second are independent events. (3) (Total 10 marks) Win1st Win2nd 0.3 0.2 0.1 0.4 Reading the results directly off the Venn diagram (a) P( Does not win either ) 0.4 (b) P(Wins exactly one ) 0.3 0.1 0.4 P (w 2 w1¹) (c) P (w 2 | w1¹) P (w1¹) 0.1 0.5 0.2 (d) P (W1 W2 ) 0.2 P (W1) P (W2 ) 0.5 0.3 0.15 P (W1 W2 ) P (W1) P (W2 ) Not independent Page 3 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions 3. A company assembles computers using components from two sources. Goodgear supplies 85% of the components and Buyrite supplies the rest. It is known that 3% of the components supplied by Goodgear are faulty and 6% of those supplied by Buyrite are faulty. (a) Represent this information on a tree diagram. (3) An assembled computer is selected at random. (b) Find the probability that it is not faulty. (3) (Total 6 marks) (a) Let G= Produced by Goodgear Let B= Produced by Buyrite Let F = Faulty component F 0.03 0.85 G 0.97 F’ 0.06 F 0.15 B 0.94 F’ (b) P (F¹) P (G F¹) P (B F¹) P (G ).P (F¹|G ) P (B).P(F¹|B) 085 0.97 0.15 94 0.966 ( 3 SF ) Page 4 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions 4. A group of 100 young people were asked which teen magazine they enjoyed reading. 30 said they read Anna, 26 read Beat, 21 read Chillout, 5 said they read both Anna and Beat, 7 both Beat and Chillout, 6 read both Chillout and Anna, and 2 said that they read all 3. (a) Represent these data on a Venn diagram. (6) A person was selected at random from this group. Find the probability that this person reads (b) at least one of the magazines (2) (c) only Anna (1) (d) only one of the magazines (2) (e) Anna, given that he reads only one of the magazines (3) (Total 13 marks) (a) A B 21 3 16 C C 2 5 4 10 39 C C Page 5 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions 61 (b) P( At least one ) 100 21 (c) P( Only A ) 100 21 16 10 (d) P ( Only one ) 100 47 100 21 (e) P( A given only one ) 47 Page 6 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions 5. A teacher calculates that if a student regularly completes their homework then the probability that they will pass the end of unit test is 0.9, but if the student fails to do homework the probability of passing is only 0.3. The teacher notes that only 75% of students regularly do their homework. A student was selected at random from this group. Find the probability that this student (a) does not do homework and passes the exam (2) (b) passes the exam (3) (c) Given that the student actually failed the exam, what is the probability that they in fact regularly completed their homework (4) (Total 9 marks) (a) Let H= Student completes homework P= Passes unit test P 0.9 0.75 H 0.1 P’ 0.3 P 0.25 H’ 0.7 P’ Page 7 of 8 EDEXCEL STATISTICS 1 PROBABILITY Exam Style Questions & Worked Solutions (a) P (H¹ P) P (H¹).P(P|H¹) 0.25 0.3 0.075 (b) P (P ) P (H P ) P (H¹ P) P (H ).P (P|H ) P (H¹).P (P|H¹) 0.75 0.9 0.25 0.3 0.75 P (H P¹) (c) P (H|P¹) P (P¹) 0.75 0.1 0.25 0.3 Page 8 of 8

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posted: | 2/20/2011 |

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