If a player rolls two dice and gets a sum of 2 or 12, she wins $20. If the perso

Question

If a player rolls two dice and gets a sum of 2 or 12, she wins $20. If the person gets a 7, she wins $5. The cost to play the game is $3. Sample space of two dice (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4. 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6,2) (6, 3) (6, 4) (6, 5) (6, 6) a. Construct a probability distribution of the game b. Find the expected value of the game c. Find the standard deviation of the game.

Explanation / Answer

let X is expected value :

hence P(X=20) =P(probability of 2 or 12) =2/36=1/18

P(X=5) =P(of 7 ) =6/36=1/6

and P(X=-3) =1-2/36-6/36 =28/36=7/9

b) from above

hence expectecd value =-0.39

c) std deviation =(33.39-(-0.39)2)1/2 =5.7652

x P(X) xP(X) x^2P(X) 20 1/18 1.11 22.22 5 1/6 0.83 4.17 -3 7/9 -2.33 7.00 Total 1      -0.39 33.39

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