2. While on vacation in Las Vegas, late one night in a bar you meet a sharply dressed man who claims to know that at the Tropicana there are six rigged slot machines in the back of the casino: four of them pay out 10% of the time (G = the good machines), and the other two pay out 20% of the time (A = the awesome machines). The six machines are all red, sitting side by side in the northeastern corner of the casino. The only problem is that the man is quite drunk, so he can't quite remember which one is which. Let N be the event where a machine doesn't pay out, and P be the event where a machine does pay out. Note: Round to 3 decimal places. You won't be penalized for cascading mistakes (a) (3 points) The next day you go to the Tropicana to find out more. You find the six machines sitting in the back of the casino, and roll a fair six-sided die to determine which you will try. Calculate P(A), the probability you select an awesome machine, and P(G), the probability you select a good machine. (b) (4 points) Calculate the probability that the machine you select pays out. (c) (4 points) If the machine you select pays out, what is the probability that it is the awesome slot machine? (d) (4 points) If the machine you select does not pay out, what is the probability that it is the awesome slot machine?