There are three dice. One die is fair. One die has fives on all six sides. One d

Question

There are three dice. One die is fair. One die has fives on all six sides. One die has fives on three sides and fours on three sides. A die is chosen at random. It comes up five. (a) What is the probability to get a five (b) Find the probability that the chosen die is the fair one. The following dice game costs $10 to play and assume the dice is fair. If you roll 1, 2, or 3, you lose your money. If you roll 4 or 5, you get your money back. If you roll a 6 win you $24. a) Find the distribution of your winnings W. b) Find the expected value of the game.

Explanation / Answer

probabilty of 5 on fair die =1/6

probabilty of 5 on second dice =1

and five on third die =1/2

probabilty of 5 on die =P(fair die chosen and five apperas+second die chosen and 5 comes +second die and 5 appears)=(1/3)*(1/6)+(1/3)*1+(1/3)*(1/2)=0.5555

b)probabilty that die was fair =(1/3)*(1/6)/0.5555 =0.1

2)probabilty of losing $10 =P(X=-10) =3/6 =1/2

P(X=0)=2/6

P(X=24)=1/6

b) expected value =(1/2)*(-10)+(2/6)*(0)+(1/6)*(24)=$-1

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