Chevalier de Mere, a French nobleman of the seventeenth century, reasoned that in a single throw of

Question:

Chevalier de Mere, a French nobleman of the seventeenth century, reasoned that in a single throw of a fair die, P(1) = 1/6, so in two throws, P(1 appears at least once) = 1/6 + 1/6 = 1/3. What is wrong with the above reasoning? Use the sample space of Exercise 4.21 to obtain the correct answer.