Answer:
0.1515 = 15.15% probability that the first two songs that play are both country songs
Step-by-step explanation:
Songs are not repeated, which means that they are chosen without replacement, and the hypergeometric distribution is used.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
His playlist contains 5 country songs, 3 alternative songs, and 4 hip-hop songs. What is the probability that the first two songs that play are both country songs?
5 + 3 + 4 = 12 total musics, which means that
5 country, which means that
First two, which means that
The probability is P(X = 2). So
0.1515 = 15.15% probability that the first two songs that play are both country songs