Question 12 (iii) - End-of-Chapter Exercises - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Question 12 (iii) Write the sample space and calculate the probability based on the given information. (iii) Three coins are tossed. What is the probability that the first coin shows heads and exactly two heads occur in total? Since 3 coins are tossed Our Sample Space would be S = {HHH, HHT, HTH, HTT, TTT, THT, TTH, THH} We need to find probability that the first coin shows heads and exactly two heads occur in total So, First coin show heads, and two heads show in total = {HHT, HTH} Thus, Required Probability = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠) = 2/8 = 𝟏/𝟒