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

Transcript

Question 7 (i) A tyre company records distances before replacement in 1000 cases. Find the probability that a randomly chosen tyre lasts: (i) Less than 4000 km. Now, Probability tyre lasts less than 4000 km = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠 𝑤ℎ𝑒𝑟𝑒 𝑡𝑦𝑟𝑒 𝑙𝑎𝑠𝑡𝑠 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 4000 𝑘𝑚)/(𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑠𝑒𝑠) = 20/1000 = 0.02 Question 7 (ii) A tyre company records distances before replacement in 1000 cases. Find the probability that a randomly chosen tyre lasts: (ii) Between 4000 and 14000 km. Now, Probability tyre lasts between 4000 and 14000 km = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠 𝑤ℎ𝑒𝑟𝑒 𝑡𝑦𝑟𝑒 𝑙𝑎𝑠𝑡𝑠 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 4000 𝑎𝑛𝑑 14000 𝑘𝑚)/(𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑠𝑒𝑠) = █(𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒄𝒂𝒔𝒆𝒔 𝒘𝒉𝒆𝒓𝒆 𝒕𝒚𝒓𝒆 𝒍𝒂𝒔𝒕𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝟒𝟎𝟎𝟏 𝒕𝒐 𝟗𝟎𝟎𝟎 @+ 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇𝒄𝒂𝒔𝒆𝒔 𝒘𝒉𝒆𝒓𝒆 𝒕𝒚𝒓𝒆 𝒍𝒂𝒔𝒕𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝟗𝟎𝟎𝟏 𝒕𝒐 𝟏𝟒𝟎𝟎𝟎)/(𝑻𝒐𝒕𝒂𝒍 𝒄𝒂𝒔𝒆𝒔) = (210 + 325)/1000 = 535/1000 = 0.535 Question 7 (iii) A tyre company records distances before replacement in 1000 cases. Find the probability that a randomly chosen tyre lasts: (iii) More than 14000 km. Now, Probability tyre lasts more than 14000 km = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠 𝑤ℎ𝑒𝑟𝑒 𝑡𝑦𝑟𝑒 𝑙𝑎𝑠𝑡𝑠 𝑚𝑜𝑟𝑒 𝑡ℎ𝑎𝑛 14000 𝑘𝑚)/(𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑠𝑒𝑠) = 445/1000 = 0.445