Non-Fungible Tokens (NFTs) are digital images that are bought, sold, and traded much like digital trading cards. Like trading cards, many NFTs are associated with sports and star athletes. NFTs sometimes sold in "blind" packs, so that the buyer doesn't know what specific images are included in the pack. These "blind" packs may include particularly sought-after (and so more valuable) images with some advertised probability. Consider an offering of "blind" packs of 8 NFTs advertising a 7.5% chance that each NFT is sought-after.

a. What is the probability that a randomly-selected pack does not include a sought-after NFT?

b. What is the probability that a randomly-selected pack includes at least one soughtafter NFT?

c. Now consider someone who buys 5 "blind" packs. Based on the probability from part (b) what is the expected number of those "blind" packs that would include at least one sought-after NFT?

d. For the buyer of 5 "blind" packs, what is the probability that none of those packs includes a sought-after NFT?

e. For the buyer of 5 "blind" packs, what is the probability that all of their packs include a sought-after NFT? If someone brags on a discussion board that s/he bought 5 "blind" packs and that all of them included at least one sought-after NFT, does this mean that the advertised 7.5% chance that each NFT is sought after is wrong? Briefly explain why or why not?