Answer to Question #180166 in Statistics and Probability for Basil Powell

Question

Mwema plays a game in which a fair die is thrown once. If the score is 1,2or 3 Mwema loses £10. If the score is 4 or 5 Mwema wins £x..If the score is 6, Mwema wins £2x.

      (i) Show that the expectation of Mwema’s is£ ( in a single game

Answer 1

Due to the fact that the chances of each roll are equal to one-sixth, we simply sum up the results of all throws and divide by six:

$\frac{1}{6}(-10-10-10+x+x+2x)=\frac{2}{3}x-5$