Year 10 Probability Revision PDF

***Probability Revision*** **Name:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Multiple choice Circle ONE correct answer (Tech)** A. [\$\\frac{3}{16}\$]{.math.inline} B. [\$\\frac{1}{6}\$]{.math.inline} C. [\$\\frac{11}{32}\$]{.math.inline} D. [\$\\frac{21}{32}\$]{.math.inl...

***Probability Revision*** **Name:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_** **Multiple choice Circle ONE correct answer (Tech)** A. [\$\\frac{3}{16}\$]{.math.inline} B. [\$\\frac{1}{6}\$]{.math.inline} C. [\$\\frac{11}{32}\$]{.math.inline} D. [\$\\frac{21}{32}\$]{.math.inline} If a 20-cent coin is tossed in the air twice, the probability of obtaining two heads is: A. [\$\\frac{1}{2}\$]{.math.inline} B. [\$\\frac{1}{4}\$]{.math.inline} C. [\$\\frac{3}{4}\$]{.math.inline} D. [\$\\frac{1}{8}\$]{.math.inline} A. [\$\\frac{4}{5}\$]{.math.inline} B. [\$\\frac{3}{4}\$]{.math.inline} C. [\$\\frac{8}{25}\$]{.math.inline} D. [\$\\frac{1}{10}\$]{.math.inline} A. 0.12 B. 0.7 C. 0.58 D. 0.92 **Section 2 Short Answer/ Extended questions** **Question 1 (7 marks) (Tech Free)** **Consider the following universal set and the events A and B.** ε= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 } A = {3, 6, 9, 12, 15} B = {2, 4, 6, 8, 10, 12, 14} a. Represent the events A and B in a Venn diagram 2 marks b. List the sets i. ii. i. ii. iii. **Question 2 (3 marks) (Tech Free)** A spinner numbered 1 to 4 is spun twice. a. List the sample space using a table 2 mark b. Find the probability that the sum of the two numbers is 6. 1 mark c. Finding the probability of obtaining a double 1 mark **Question 3 (6 marks) (Tech)** In a particular school 45% of students are female ([*F*]{.math.inline}). Of the female students 18% say mathematics ([*M*]{.math.inline}) is their favourite subject. While of the non female students ([*F*']{.math.inline}) 13% prefer mathematics. a. Construct a tree diagram to represent the above and include **all probabilites and outcomes**. 3 marks Outcomes Probabilities b. Find the probability that i. a student chosen at random prefers mathematics and is female. 1 mark ii. a student chosen at random prefers mathematics. 2 marks **Question 4 (5 marks) (Tech Free)** a. Complete the given two way table. 2 marks -- -- -- -- -- -- -- -- b. Using the table above, find the following: i. ii. iii. **Question 5 (Tech or Tech Free)** Fifty teenagers were asked what they did at weekends. A total of 35 said they went to football matches, movies or both. Of the 22 who went to football matches, 12 said they went to movies. **F is the event \"a teenager goes to the football\", and M the event: "a teenager goes to the movies\".** **(a)** Illustrate using a Venn diagram **2 marks** b\. Find the following probabilities: i. [*Pr*(*F*′)]{.math.inline} **1 mark** ii. [*Pr*(*F*′*M*′)]{.math.inline} **1 mark** iii. [*Pr*(*FM*)]{.math.inline} **1 mark** iv. [*Pr*(*F*\|*M*′)]{.math.inline} **(c)** **Prove** that F & M are not independent events. 3 marks **Question 6 (5 marks) (Tech)** Athletics is compulsory at a certain school. Students may participate in sprints (S), middle distance events (M) or field events (F). 5 students participates in all three types of event, but 180 students are involved in both S and M, 50 are involved in both M and F, and 80 in both S and F. There are 520 students who do sprints, 470 do middle distance and 280 do field events. a. Represent this information as a Venn diagram. 2 marks b. How many students are at the school? 1 mark c. If one student is chosen at random, find the probability that this student ii. **Question 7 (2 marks) (Tech Free)** Two events, *A* and *B*, have the following Venn diagram showing the number of elements in each set. Also [*n*(*A*′∩*B*) = *x*]{.math.inline} where [x ]{.math.inline}is a positive integer. For what value of, x, are events *A* and *B* are independent, i.e. Pr(*A* \| *B*) = Pr(*A*) **Question 8 (9 marks) (Tech)** A survey of 250 Yr 10 students was conducted to investigate their eating habits. They were asked which of the following cuisines they eat; Italian, Asian or traditional Anglo Saxon. These statistics were obtained: - 50 eat all three cuisines - 20 eat Traditional Anglo Saxon only - 29 eat Italian and Asian but not Traditional Anglo Saxon - 38 eat Italian and Traditional Anglo Saxon but not Asian - 70 eat Asian and Traditional Anglo Saxon - 30 eat Asian only - 15 do not eat any of the three types of cuisine a. Use the above information to fill in the following Venn diagram 2 marks b. If one of the students surveyed is selected at random, what is the **probability** that he or she: i. eats Italian **. 1 mark** ii. eats Italian and Traditional Anglo Saxon **1 mark** iii. does not eat Asian **1 mark** iv. eats Traditional Anglo Saxon only **1 mark** v. eats Italian given that he/she eats Asian **1 mark** c. **Are the events of and eating Italian and eating Asian independent events? Prove it.**