Question

Show all work, and staple your work together. Draw all trees. You take your significant other to the carnival. There are many games to play, each game costs $5. You have a chance to win a stuffed bear for your significant other. The games are as follows: A-You draw 1 card from a standard deck of 52 cards, and flip a coin. You win if the card is a CLUB or you get TAILS on the coin. B-You pull a number from a uniform distribution, U(7,21). If the value is under 15 OR above 10, your final draw is from a normal distribution X™N(5, 7). Otherwise, your final draw is from Y*N(2,2). You win if your final draw is positive. First, draw trees for game A, B. (Hint: Simplify the trees, don't draw 52 branches.) Evaluate the probability of: 1. Getting a CLUB in game A. 2. Getting a TAILS in game A. 3. Winning Game A. 4. Losing Game A. 5. Drawing from distribution X. 6. Drawing from distribution Y. 7. Getting a positive number given you are drawing from distribution X, P(result > 0 X). 8. Getting a positive number given you are drawing from distribution Y, P(result > 0 1Y). 9. Winning game B. 10. Losing game B when drawing from Y. 11. Which game should you play to maximize your chances of winning the stuffed bear?

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Answer 1

There are total 52 cards and 13 clubs "Plobetting a club ingame A) ② Plgetting a tails) = 12 p (winning game A) =P ( getting a club or getting tails) = P(getting a club) + P(getting tails) game A) © P(lossing game A) = 1- P(winning al = 0.25 h PC drawing from distributions) = P(10<2<15 where ZN U (7,21)) = P(3215) - P(Z<10) 1P (2-2)= P(2615) = 15-7 21-7 21-7 19 © (2410) P (drawing from distribution) = 1- P (drawing from distributionx) 21-7 - 1- 5 = 24 6 ~ N (5,7) .X ~ N(01) le z~ N(0,1) P(x>0) =P ( x 5 x 5 ) =P(z) - 1.88) 161-1.88) = 0.969946 V

YAN(2, 2) ie Y-2 NN(Old V2 j.e. ZnN601) P(yo) = P(Y-2 -2) = P(2 7-82) = 1- $(-22) V2 = 0.921319 O P (winning game B) = P(result so lx) X+ P (result >oly) = P(X70XP (yo) (as both can't occartogether) = 0.ataqu6x0.921319 - 0.8996296788 107 P ( losing game when drawing fromy) = P(y2O) = 1- P(770) = 1-0.921319 = 0.078681 (11) P(winning game A) = 0.75 P (winning game B) = 0.8936 70.ts :. I should play game & B to maximize the chance of winning stuffed bear.