Question

You now work at a casino in Las Vegas. You have been told that the settings on the machines are different. Your probability of winning in every round on one machine is 23.9%. The other machine offers the probability of winning equal to 2.1% in every round.

You are going to test the machines. You walk up to the 2 machines but you dont know which is which, so your chance of selecting the higher chance machine is 50%

a. Draw a tree diagram to describe this experiment (first you select the machine, then you either win of lose).

b. What are the chances that you would win in the next round.

c. You’ve played two rounds and you won both times. What is the revised probability that you are playing on the machine with higher winning ratio, given these results.

Answer 1

a). Tree diagram for the experiment. (w/m) 23.9% win 50% mi? Higher chance machine 76014 Lose : e Lower chance 201% win (W/m2) 50% Machine 94.91% Lose The chance of of we would in the next round b) c) ا عمال Higher chance machine = 50% x 23.9% = 10.1195 (Sox 239) Lower chance machine = 50%x 2014 - Lo.o105] (Soome) The probability that we win both rounds we play. = (0.1195 x 0.1195) + o.olos X 0.0105 ) =0.0143905 for Highes machine for lowerchance (Total winning probability The revised probability that we are playing on the machine with higher winning ratio given that we won both times = 0.1195 00:1195 -0.01428025 0.0143905 The probability is = 0.9923387 = [0,9923 Machine 0.0143905 P ( nap/w) = P (MA) P (WDM1) pim.prwmot p (m2).plwm) Baye's jule for posterior probability