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?

Question

Mathematics

Hill

7 February, 01:01

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?

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Answers (1)

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Cynthia Fitzgerald · Answer 1

-0.075

Step-by-step 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