Sam is playing songs on her mp3 player. She has 7 hip-hop songs, 9 rock songs, and 7 pop songs. If she has the mp3 player play the songs at random without repeating, what is the probability that the first song will be a rock song and the second song will be a hip-hop song?
If there are N songs in total, then
P(rock,hip) = #rock/N * #hip/(N-1)
To find the probability of the first song being a rock song and the second song being a hip-hop song, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of songs = 7 (hip-hop songs) + 9 (rock songs) + 7 (pop songs) = 23 songs
Since the songs are played at random without repeating, the total number of possible outcomes is 23.
Favorable outcomes: We want the first song to be a rock song, which means we have 9 rock songs to choose from. After selecting a rock song, we want the second song to be a hip-hop song, and we have 7 hip-hop songs to choose from.
Therefore, the number of favorable outcomes is 9 (rock songs) * 7 (hip-hop songs) = 63.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
P(rock, hip-hop) = Favorable outcomes / Total outcomes
= 63 / 23
Therefore, the probability that the first song will be a rock song and the second song will be a hip-hop song is approximately 2.74 or 2.74/100.
To find the probability of the first song being a rock song and the second song being a hip-hop song, we need to divide the number of favorable outcomes (rock song followed by a hip-hop song) by the total number of possible outcomes.
Let's calculate the number of favorable outcomes first:
The number of rock songs is 9.
After playing a rock song, there will be 8 rock songs left.
Out of the remaining 8 rock songs, 7 will be hip-hop songs.
So, the number of favorable outcomes is 9 * 7 = 63.
Now, let's calculate the total number of possible outcomes:
The total number of songs is 7 + 9 + 7 = 23.
Since the first song is chosen randomly and without replacement, there are 23 choices for the first song, and after that, there are 22 choices for the second song.
Therefore, the total number of possible outcomes is 23 * 22 = 506.
Finally, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 63 / 506 ≈ 0.1245
Therefore, the probability that the first song is a rock song and the second song is a hip-hop song is approximately 0.1245, or 12.45%.
What is (9/23)(7/22) ?
assuming that the player will not play the same song two times in a row.