In October 2020, the YouTuber called "Dream" posted a speedrun of Minecraft and was accused of cheating.

In Minecraft, when you trade with a piglin, the piglin gives you an ender pearl 4.7% of the time. Dream got 42 ender pearls after 262 trades with piglin.

1. If you trade 262 times, what is the expected number of ender pearls you receive?
2. What is the probability of getting 42 or more ender pearls after 262 trades?

When you kill a blaze, you have a 50% chance of getting a blaze rod. Dream got 211 blaze rods after killing 305 blazes.

1. If you kill 305 blazes, what is the expected number of blaze rods you receive?
2. What is the probability of getting 211 or more blaze rods after killing 305 blazes?
3. Do you think Dream was cheating?