You are watching: You roll a die. if it comes up a 6 you win $100

Click right here to watch ALL problems on Probability-and-statisticsConcern 698017: Roll a die. If you roll a 6 then you win $100, if you execute not roll a 6 then you obtain to roll again. If you roll a 6 then you win,If you perform not roll a 6 on the second attempt you loose and game stops.What is the meant value of this game? Answer by Positive_EV(69) (Show Source): You deserve to put this solution on YOUR website! The intended worth of the game is equal to the sum of the commodities of each outcome and also its corresponding probability. You do not specify just how much you lose if you perform not roll a 6 at any kind of allude - this is necessary for the calculation. For the functions of this difficulty I will assume that a loss has a result of $0, and also a win has an outcome of $100.The probability that you roll a 6 on either roll is equal to the probcapability that you roll a 6 on the initially roll + the probcapability that you roll a 6 on the second roll. If the die has actually 6 sides, there is 1 side out of 6 that wins, so the probcapability of rolling a 6 on the first roll is 1/6.The probability that you roll a 6 on the second roll is additionally 1/6; but, if you roll a 6 on the initially roll you do not must roll twice. The probcapacity of gaining a 6 on the second roll is for this reason the probcapability that you necessary a 2nd roll times the probcapacity that you roll a six on the second roll; that is, the probcapacity that the initially roll is not a 6 and also the second roll is. For the initially roll, tright here are 5 non-6 numbers out of 6, so the probcapacity that you require a 2nd roll is 5/6. Because of this, the probcapacity that you win on the second roll is (5/6)*(1/6) = 5/36.The probcapability that you win is the sum of these probabilities, 1/6 + 5/36 = 11/36. The occasion that you shed is the compliment of the occasion that you win, so its probcapability is 1 - P(win) = 1 - 11/36 = 25/36.Last, the intended worth is the sum of the assets of the results and also their probabilities, which is (11/36)*100 + (25/36)*0 = ~$30.56, assume you lose nopoint if you shed.

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If you shed some dollar amount $X once you shed, this formula alters to (11/36)*100 + (25/36)*(-X).