Question 9 - End-of-Chapter Exercises - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Question 9 (i) A game of chance consists of spinning an arrow (see Fig. 7.7.) which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at (i) 8? Total numbers = 8 Number of times we can get 8 = 1 Now, Probability of getting 8 = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑤𝑒 𝑐𝑎𝑛 𝑔𝑒𝑡 8)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠) = 𝟏/𝟖 Question 9 (ii) (ii) An odd number? Odd numbers in game = 1, 3, 5, 7 Number of odd numbers = 4 Now, Probability of getting odd number = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 ) = 4/8 = 𝟏/𝟐 Question 9 (iii) (iii) A number greater than 2? Number greater than 2 = 3, 4, 5, 6, 7, 8 Number of numbers greater than 2 = 6 Probability of getting number greater than 2 = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 2)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 ) = 6/8 = 𝟑/𝟒 Question 9 (iv) (iv) A number less than 9? Number less than 9 = 1, 2, 3, 4, 5, 6, 7, 8 Number of number less than 9 = 8 Now, Probability of getting number less than 9 = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 9)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 ) = 𝟖/𝟖 = 1 Question 9 (v) (v) A multiple of 3? Multiples of 3 are 3, 6, 9, 12, 15, …. Multiples of 3 possible in outcome = 3, 6 Number of numbers which are multiples of 3 = 2 Now, Probability of getting multiple of 3 = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑤ℎ𝑖𝑐ℎ 𝑎𝑟𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒𝑠 𝑜𝑓 3)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 ) = 𝟐/𝟖 = 𝟏/𝟒