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Jenny has a playlist on her phone. her playlist consists of 60 songs. Jenny thinks one specific song will play after the one she listens to. What are her chances of being right in percentage and fraction form?

7 answers

If Jenny has a playlist of 60 songs and is listening to one song, there is only one specific song that she thinks will play next. Therefore, there is 1 favorable outcome (the song she thinks will play) out of 59 possible outcomes (the other songs that could play next, excluding the one currently playing).

To calculate the chances of her being right:

  1. Fraction Form: The probability is given by the ratio of favorable outcomes to total possible outcomes: \[ \text{Probability} = \frac{1}{59} \]

  2. Percentage Form: To convert the fraction to a percentage, you multiply by 100: \[ \text{Percentage} = \left( \frac{1}{59} \right) \times 100 \approx 1.6949% \]

Thus, Jenny's chances of being right are approximately \( \frac{1}{59} \) in fraction form and about \( 1.69% \) in percentage form.

Wow. Jenny's chances are slim. What if the song she listened to was in a playlist of 17? what are her chances then?

If Jenny has a playlist of 17 songs and she is listening to one song, there is still only one specific song that she thinks will play next. Therefore, there are 16 other songs that could play next, making the total number of possibilities 16.

  1. Fraction Form: The probability that the specific song plays next is: \[ \text{Probability} = \frac{1}{16} \]

  2. Percentage Form: To convert the fraction to a percentage, multiply by 100: \[ \text{Percentage} = \left( \frac{1}{16} \right) \times 100 \approx 6.25% \]

Therefore, if Jenny's playlist has 17 songs, her chances of being right are \( \frac{1}{16} \) in fraction form and \( 6.25% \) in percentage form.

Still a long shot. What if her playlist has 7 songs in it?

If Jenny has a playlist of 7 songs and she is listening to one song, there are 6 other songs that could play next. Since she is thinking of one specific song, there is only 1 favorable outcome.

  1. Fraction Form: The probability that the specific song plays next is: \[ \text{Probability} = \frac{1}{6} \]

  2. Percentage Form: To convert the fraction to a percentage, multiply by 100: \[ \text{Percentage} = \left( \frac{1}{6} \right) \times 100 \approx 16.67% \]

Therefore, if Jenny's playlist has 7 songs, her chances of being right are \( \frac{1}{6} \) in fraction form and approximately \( 16.67% \) in percentage form.

Still a coin toss, but still, she has a chance.

Absolutely! With a smaller playlist of 7 songs, Jenny's chances are considerably better compared to larger playlists. With \( \frac{1}{6} \) or about \( 16.67% \), she has a reasonable shot of guessing correctly. As the playlist size decreases, the probabilities indeed become more favorable. If you have any further questions or scenarios you'd like to explore, feel free to ask!