QUESTION 10.00 Copy of Suppose you have a six sided die. One face is printed wit

Question

QUESTION 10.00 Copy of Suppose you have a six sided die. One face is printed with the number 1. Two faces are printed with the number 2. Three faces are printed with the number 3. You also have 3 coins: C1, C_ 2, and C3. C_1 will land Heads with probability 1/4 C_2 will land Heads with probability 1/2 C3 will land Heads with probability 1/3. You roll the die. If the die lands with a 1 face up, flip coin C 1 If the die lands with a 2 face up, flip coin C 2 If the die lands with a 3 face up, flip coin C 3 1. (2.5 points) What is the probability that the tossed coin lands Heads? 2. (2.5 points) What is the probability that the die landed on a 1 given the tossed coin lands Heads? 3.(2.5 points) Every time you play the game, you win when you get Heads. What is the probability of winning the game for the first time on the 5th attempt? 4. (2.5 points) Every time you play the game, you win when you get Heads. The amount you win is the number shown on the toss of the die. What are your expected winnings for playing the game?

Explanation / Answer

1)P(heads)=P(1on die and heads)+P(2on die and heads)+P(3on die and heads)

=(1/6)*(1/4)+(2/6)*(1/2)+(3/6)*(1/3)=3/8

2)

P(C-1|heads)=P(1on die and heads)/P(heads)=(1/6)*(1/4)/(3/8)=1/9

3)

P(winning first on 5th attempt)=(1-3/8)4*3/8=0.05722

4)

expected winning =1*P(1on die and heads)+2*P(2on die and heads)+3*P(3on die and heads)

=1*(1/6)*(1/4)+2*(2/6)*(1/2)+3*(3/6)*(1/3)=0.875

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