5. You did tell Professor Zhang you were going to do research on probabil- ity. You just happen to be in Las Vegas when doing it. "It's half-true," you attest. "It's also half-false," says Alice. "Maybe he should give you half of your A." After you solved Alice's box problem, the only thing really stopping her plans was the remaining funding. Her last client is the Wynns Casino. "If Eve keeps rigging our slot machines, we'll go out of business and be taken over by the big evil corporate casinos... we're a 'mom and pop' casino and provide local jobs. You have to help us!" was their message. "Are we even the good guys here?" You wondered, "I mean, aren't they a corporation too, just a small one? And don't even the big casinos provide local jobs?" You shake your head. "I'm so confused." "These are good questions." She finally replied after about a minute of quiet walking. You met Clarence, a "reliable source," to explain the situation. It seems that after Eve hacked her way into the casino, the Wynns ended up with 2 kinds of slot machines: one that wins 5% of the time (a "normal" machine) and one that wins 40% of the time (a "rigged" machine). They were also color-coded by a colored sticker under the machine, so one kind had a white panda sticker and one kind had a black panda sticker. Unfortunately, your reliable source was also reliably drunk, so Clarence doesn't remember which color corresponded to which. "It's 50-50." He burped. The slot machines were closed off behind yellow ropes to appease a horde of gamblers who had already had a taste of beating the house. You estimate you only have about 2 hours before they turn rabid. The line snaked way past the yellow ropes and lead all the way back to the street. An old man in a (new) red jacket stared at the corner machines, beamed with so much hope that his wrinkles were invisible behind the radiance. A lady with hawkish eyes in a sky-blue dress perched, practically salivating. A very thin boy with a blue-and-yellow basketball jersey just finished his sandwich. His father had kept him to hold the spot in line, with the sandwich as payment. You wove through the line, through a gauntlet of icy glares, are they cutting??", and swampy odor. The casino guard finally succeeded in getting you and Alice in front of 2 machines. You crouched. Sure enough, one machine had a white panda sticker and one had a black panda sticker. "Well, as Clarence says, it's 50-50 right?" you reached for your wallet. Alice nodded, pulled out her ready dollar bill, and slipped it into the white-panda machine. The machine blooped. "Sorry, you lose." "Not 50-50 any more," Alice said, and she then gave her new probability estimate on the machine colors. "That seems right." You agreed after a bit of thinking. You really do need to dust up on your fundamentals. Ugh. Was there anything smart you could say in this situation? "You know, if you draw an 'A' with a flat top and the two vertical lines more vertically, half of an 'A' is literally an 'F'." Alice correctly computed the current probability that white-panda ma- chines (as opposed to black-panda machines) are the rigged machines. What is this probability? Problem part 2: Suppose you also put in your bill and it also "lost." What is the probability now?