2018 TJC MYCT P2 Q11

A new radio station broadcasts only popular hit songs from the 1980s and 1990s. Tuck Wah, who is very familiar with songs from that era, is able to correctly identify \(80\%\) of the songs aired by the station.

1. Find the smallest value of \(n\) such that, out of \(n\) songs aired by the station, the probability that Tuck Wah is unable to correctly identify at most one song is less than \(50\%\).[3]

The radio station has a regular feature – an uninterrupted sequence of \(9\) randomly selected songs aired without advertisement breaks. \(4\) such sequences are played daily.

2. Find the probability that Tuck Wah is able to correctly identify at least \(5\) out of \(9\) songs in a randomly selected sequence.[2]
3. Find the probability that Tuck Wah is unable to correctly identify any two consecutive songs in a randomly selected sequence, given that he is able to correctly identify at least \(5\) out of \(9\) songs in that sequence.[3]
4. Find the probability that in a month of \(30\) days, Tuck Wah is able to correctly identify an average of at least \(7\) songs in a sequence.[5]