3. [5 points] George Martin loves The Beatles. Honestly, who doesn't? On George's favorite Spotify playlist, 40% of the songs are by The Beatles. During a long road trip, George shuffled his playlist and listened to
30 songs. What is the probability that at least half of the songs on the trip were by The Beatles? Don't
forget to check appropriate conditions before you do your computations. Note: you can assume the
playlist is infinite in length.
4. [5 points] You have two large bins of several thousand plastic beads. Bin A is 60% red beads; bin B is
48% red beads. Suppose you select 80 beads from each bin. What is the probability that the proportion of
red beads selected from bin B is greater than the proportion of red beads selected from bin A? Don't
forget to check appropriate conditions before you do your computations.