Questions: Question John has a music list containing 32 songs. There are 5 country songs, 7 rock, 9 classical, 8 jazz, and 3 rap. What are the odds that a rock song is not selected at random?

Solution Steps

To find the odds that a rock song is not selected, we first determine the total number of songs that are not rock songs. Then, we calculate the probability of selecting a non-rock song by dividing the number of non-rock songs by the total number of songs. Finally, we express this probability as odds.

To find the number of non-rock songs, subtract the number of rock songs from the total number of songs: \[ \text{non\_rock\_songs} = \text{total\_songs} - \text{rock\_songs} = 32 - 7 = 25 \]

The probability of selecting a non-rock song is given by the ratio of non-rock songs to the total number of songs: \[ P(\text{non-rock}) = \frac{\text{non\_rock\_songs}}{\text{total\_songs}} = \frac{25}{32} \approx 0.7813 \]

The odds of selecting a non-rock song are calculated by dividing the probability of selecting a non-rock song by the probability of not selecting a non-rock song: \[ \text{Odds}(\text{non-rock}) = \frac{P(\text{non-rock})}{1 - P(\text{non-rock})} = \frac{0.7813}{1 - 0.7813} \approx 3.571 \]

Final Answer