a) consider the first song played . The probability of its being liked is 4/9.
And for second song, we have 3 liked songs and 8 remaining songs.
Hence probability of second being liked is 3/8.
Overall probability = (4/9)*(3/8) = 1/6 = 0.167 hence it is almost unusual.
b) First song being not liked is 5/9.
And for second song being not liked is 4/8.
Hence overall probability = (5/9)*(4/8) = 5/18.
c) To like exactly one of them, it has 2 possibilities. First song may be liked and second song disliked = (4/9)*(5/8) = (5/18)
First song may be disliked and second song liked = (5/9)*(4/8) = (5/18)
Hence overall probability = (5/18)+(5/18) = 5/9
d) a)Probability of 2 songs liked by me with replacement means in both cases i have to select a song from 4 liked songs.
Hence probability = (4/9)*(4/9) = 16/81
b) probability of both being not liked by me is = (5/9)*(5/9) = (25/81)
c) probability of exactly one being liked = (4/9)*(5/9)+(5/9)*(4/9) = 40/81
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