At a carnival there is a booth with a dice game. Players pay $5 to roll two dice. If any of the dice show 6, the player wins $10. Score may change after teacher review. a. Let the random variable X = the player's profit in one play of this game. Create the probability model. Enter your P(X) values as fractions, #/#. X ty ty P(X) ty ty b. Find the expected value of the random variable. E (X) = $ type your answer... c. Interpret the expected value in context. type your answer... d. Find the standard deviation.

You are on a TV show. You have been asked to either play a dice game five times or accept a $120 bill. The dice game works like this: If you roll a 1 or 5, you win $50. If you roll a 4, you win $150. If you roll a 2, 3 or 6, you lose $30. Should you play the game? Answer yes or no. __________ Use expected values and decision theory to justify your answer. Please round the answer to two decimal places. Expected value of five games is $__________

You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent

tab Carlos buys a bax of doughnuts. The box contains 9 chocolate glazed, 5 Boston crème, and 7 powdered sugar doughnuts. He reaches into the box and randomly selects a doughnut, then reaches into the box again and selects another doughnut. What is the probability that he randomly selects a Boston crème first and then a chocolate glazed doughnut? Round your answer to three decimal places. esc ps lock ! 1 Q F1 A 2 F2 W S #3 80 F3 E D $ 4 Q F4 R F % 5 0 F5 T : ^ 6 G G F6 Y C & 7 H ‹k F7 U * 00 8 N F8 ( 1 DD 9 F9 JK M ) 0- O 72 F10 < 4 P F11 ^ + F12 = [ 11 S I