Now that weddings can be held again you end up being invited to one and you decide to observe the musical taste of the guests. Having observed previous weddings we can assume that each person asks for a dance track with a probability of 0.2, a pop song with a probability of 0.3, a rock song with a probability of 0.15, or a hip hop song with a probability of 0.35. Assume each guest makes one request and all of their requests are made independently.

a) If you observe 10 guests what is the chance more than half of them will choose not to select a pop song?

b) If there were 150 guests at the wedding including yourself, how many guests would you expect to have to observe before the first guest that did not select a pop song?

c) If you observe 100 guests what is the chance the first guest will choose not to select a pop song?

d) If you observe 9 guests and you also select a song yourself then what is the chance you will be the only one that selected a pop song? (Note: Assume you are also independent from the other guests and you follow the same distribution of song choice)