Question

Suppose that two​ players, R and​ C, write down letters of the alphabet. If both write vowels or both write​ consonants, then there is no payment to either player. If R writes a vowel and C writes a​ consonant, then C pays R ​$6. If R writes a consonant and C writes a​ vowel, then R pays C ​$5. Suppose that R chooses a consonant 75​% of the plays and C chooses a vowel 30​% of the plays. What is the average loss of R per​ play?

Answer 1

-0.075

Explanation:

[Player R, Player C] cases & outcomes :-

• (Vowel, Vowel) = (0,0)
• (Consonant, Consonant) = (0,0)
• (Vowel, Consonant) = (6,-6)
• (Consonant, Vowel) = (-5,5)

• Prob (R chooses consonant) = 75% = 0.75
• Prob (R chooses vowel) = 1 - 0.75 = 0.25
• Prob (C chooses vowel) = 30% = 0.30
• Prob (C chooses consonant) = 1 - 0.30 = 0.70

Average Loss of R = Expected value of : he choses consonant & C choses vowel; he chooses vowel & C choses consonant

= (0.75)(0.30)(-5) + (0.25)(0.70)(6)

-1.125 + 1.05

= -0.075