The songs on Gavin’s phone are shown in the table below - Junior Cycle Mathematics - Question 1 - 2015

To find the probability that a randomly played song is by Hozier, we use the formula for probability:

$P(Hozier) = \frac{\text{Number of Hozier's songs}}{\text{Total number of songs}}$

Hozier has 3 songs, and the total number of songs is 30.

Thus,

$P(Hozier) = \frac{3}{30} = \frac{1}{10}$

Therefore, the probability is \frac{1}{10}.

To calculate the probability that a randomly played song is by Ed Sheeran or Pharrell, we add the number of songs from both artists and divide by the total number of songs:

$P(Ed Sheeran \text{ or } Pharrell) = \frac{\text{Number of songs by Ed Sheeran} + \text{Number of songs by Pharrell}}{\text{Total number of songs}}$

The number of songs by Ed Sheeran is 4 and by Pharrell is 15:

$P(Ed Sheeran \text{ or } Pharrell) = \frac{4 + 15}{30} = \frac{19}{30}$

Thus, the probability is \frac{19}{30}.

To calculate how many different ways Gavin can play a song by Ed Sheeran and then a song by Hozier, we multiply the number of songs he has from each artist:

Number of Ed Sheeran's songs: 4

Number of Hozier's songs: 3

The total combinations are:

$4 \times 3 = 12$

Therefore, Gavin can play the songs in 12 different ways.