Respuesta :
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:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
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:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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 [tex]N = 12[/tex]
5 country, which means that [tex]k = 5[/tex]
First two, which means that [tex]n = 2[/tex]
The probability is P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,5) = \frac{C_{5,2}*C_{7,0}}{C_{12,2}} = 0.1515[/tex]
0.1515 = 15.15% probability that the first two songs that play are both country songs
