Question

STA2023 Elements of Statistics 12124 Blanka Irizarry Homework: Section 5.4 Homework Save Sco e: 0 of 1 pt 7 of 10 (10 complete) ▼ Hw Score: 78.33%, 7.83 of 10 p 5.4.27 Question Hep Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your player, each of the 12 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 12 songs are played. (a) The probablility that you like both songs is (Round to three decimal places as needed.)

Answer 1

a) you like 2 songs of 12 songs

Thus, probability of listening to a song you like if you play them randomly = 2/12 = 1/6

Thus, probability that you play two songs at random and like both = 1/6*1/6

= 1/36

= 0.028

Yes this is unusual as the probability value is less than 0.05

b. Probability you like neither

= 5/6*5/6

= 25/36

= 0.694

c. Probability you like exactly one

= You like 1st or you like 2nd

= 1/6*5/6 + 5/6*1/6

= 10/36

= 0.278