12. Imagine that, while in Mexico, you also took a side trip to Las Vegas, to pa
ID: 3072669 • Letter: 1
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12. Imagine that, while in Mexico, you also took a side trip to Las Vegas, to pay homage know to the TV show CSI. Late one night in a bar that in the casino at the Tropicana there are two sorts of you meet a guy who claims to slot machines: one that pays out 10% of the time, and one that pays out 20% of the time [note these numbers may not be very realistic]. The two types of machines are colored red and blue. The only e guy is so drunk he cant quite remember which color corresponds to ext which kind of machine. Unfortunately, that night the guy becomes the vic in the n CSI episode, so you are unable to ask him again when hes sober. Next day you go to the Tropicana to find out more. You find a red and a blue machine side by side. Since you do not know which machine pays out more often. You assume that they have the same probably to be the one that pays out. You toss a coin to decide which machine to try first; based on this you then put the coin into the red machine. It doesnt pay out. How should you update your estimate of the probability that this is the machine youre interested in? What if it had paid out - what would be your new estimate then? Let B (or R) be the event that the blue (or red) machine is the one that pays out more often. Let W (or L) be the event that the chosen machine, which is red, pays out (or doesn't pay out).Explanation / Answer
So thier are 2 cases :-
(1) If the Red machine don't pays out for the 1st time, we will try again for 4 more times. As the probability of the machine that pays more is 20% , that means, If Red one is that right machine, then the probability of pay out should be, P (W) = 20/100 =1/5.
Which means it will pay 1 time in every 5 times, so if it doesn't pays for the 1st time, we wil try again for 4 times more, if it pays in the next 4 times then this is the right machine in which we are interested and if it don't pays in the next 4 times then we will be sure that this is not the right machine.
(2) If it pays for the 1st time, then we will try again for 9 times more, if it pays out in the next 9 times then this is the right machine. As the probability of pay out is, P(W) = 1/5, so it should pay for 2 times for every 10 times coins inserted. If it doesn't pays in the next 9 times then this isn't the right machine.
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