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

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The songs on Gavin’s phone are shown in the table below. Singer Number of songs Usher Pharrell 15 Ed Sheeran 4 Hozier 3 Gavin has 30 songs on his phone, in tota... show full transcript

Worked Solution & Example Answer:The songs on Gavin’s phone are shown in the table below - Junior Cycle Mathematics - Question 1 - 2015

Step 1

Find how many songs by Usher are on Gavin’s phone.

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Answer

To find the number of songs by Usher, we can use the total number of songs and subtract the number of songs from the other artists.

Starting with 30 total songs:

Number of songs by Pharrell = 15

Number of songs by Ed Sheeran = 4

Number of songs by Hozier = 3

Calculating the sum of Pharrell, Ed Sheeran, and Hozier's songs:

15+4+3=2215 + 4 + 3 = 22

Now, subtract this from the total:

3022=830 - 22 = 8

Thus, there are 8 songs by Usher.

Step 2

Find the probability that this song is by Hozier.

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Answer

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

P(Hozier)=Number of Hozier’s songsTotal number of songsP(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)=330=110P(Hozier) = \frac{3}{30} = \frac{1}{10}

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

Step 3

Find the probability that this song is by Ed Sheeran or Pharrell.

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Answer

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(EdSheeran or Pharrell)=Number of songs by Ed Sheeran+Number of songs by PharrellTotal number of songsP(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(EdSheeran or Pharrell)=4+1530=1930P(Ed Sheeran \text{ or } Pharrell) = \frac{4 + 15}{30} = \frac{19}{30}

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

Step 4

In how many different ways can he do this?

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Answer

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:

4×3=124 \times 3 = 12

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

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