Lucy offers to play the following game with Charlie: "Let us show dimes to each other, each choosing either heads or tails. If we both show heads, I pay you $3. If we both show tails, I pay you $1. If the two don’t match, you pay me $2." Charlie reasons as follows. "The probability of both heads is 1/4, in which case I get $3. The probability of both tails is 1/4, in which case I get $1. The probability of no match is 1/2, and in that case I pay $2. So it is a fair game." Is he right? If not, (a) why not, and (b) what is Lucy’s expected profit from the game?

(a)Charlie is right

(b)$0

Step-by-step explanation:

(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.

In the game, the possible outcomes are: HH, HT, TH and TT.

Charlie wins when the outcome is HH, TT

Lucy wins when the outcome is HT or TH

Therefore, the game is fair. Charlie is right.

(b)

If the outcome is HH, Lucy pays $3.

If the outcome is HT or TH, Lucy gets $2.

If the outcome is TT, Lucy pays $1.

The probability distribution of Lucy's profit is given below:

Expected Profit

Lucy's expected profit from the game is $0.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights