random variable question - please show all work

PROBLEM (a) (b) (0} (d) (f) (g) . Stars are painted on a coke cap with probability 0.05, independently from In I 0 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. Given that a winning 6-pack contains two stars, nd the probability that the corresponding cokes are touching. :.-'\\s illustrated in the diagram: the L'Ltl'tlL'l'CtlltL'h[Eltlt'iliwutililL'l'L'UlmL'thlcI'L'lt'ltlltllllgl\\\\'t'l'lttlJL'ltlltl'L'CL11ilL']'L'UhC>~.] 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, nd 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= Is). Also, nd 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 onEy 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.)