QUESTION 4

A. In a game, a player is required to select a card while blindfolded. In the bowl there are 2 red cards and 6 black cards. A red card will earn him 5 points while a black card will earn him only 1 point. Let T represent the number of points he can possibly earn.

(i) Tabulate the probability distribution of T.

(ii) Determine the expected value and standard deviation of T.

(iii) For every point that he earns, he will be paid $5. The cost to play the game is $15. Let W be the net amount ($) that he receives. Is it worth it for him to play the game? Justify your answer using Laws of Expected Values.

(iv) Using Laws of Variance, calculate the variance of W.