(a) (b) (c) (d) (e) (f) Stars are painted on a coke cap with probability 0.05, independently from one cap to the next. A truck contains 10,200 cokes, organized into 1700 packs of 6. Find the probability that the total number of stars on the truck is more than 525. Find the probability that a 6-pack has two stars. A 6-pack is a "winning 6-pack" if it contains one or more stars. Find the probability that there are more than 470 winning 6-packs on the truck. Colaca-Cola Coca Given that a winning 6-pack contains two stars, find the probability that the corresponding cokes are touching. (As illustrated the diagram: the corner cokes touch two other cokes, the remaining two touch three other cokes.) A shopper buys four 6-packs, for a total of 24 cokes. Given that the total number of stars in these 24 cokes is 4, find the probability that they were evenly distributed across the 6- packs (i.e., one star per 6-pack). A shopper buys cokes one at a time from a vending machine until a total of 3 stars are purchased. Let the random variable Y be the total number of cokes purchased. Find its pmf Py( k) = P(Y = k). Also, find its mean E(Y). A shopper intends to purchase cokes one at a time from a vending machine until a total goal of 2000 stars is achieved. However, this shopper only has enough money to purchase 41,000 cokes. Find the probability that the shopper runs out of money before the goal is achieved. (The vending machine is constantly being restocked, it never runs out of cokes.)