Respuesta :
Answer:
(A) 0.4196
(B) 0.2398
(C) 0.0020
Step-by-step explanation:
Given,
Total songs = 15,
Liked songs = 6,
So, not liked songs = 15 - 6 = 9
If any 5 songs are played,
Then the total number of ways = [tex]^{15}C_5[/tex]
(A) Number of ways of choosing 2 liked songs = [tex]^6C_2\times ^9C_3[/tex]
Since,
[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]
Thus, the probability of choosing 3 females and 2 males = [tex]\frac{ ^6C_2\times ^9C_3}{^{15}C_5}[/tex]
[tex]=\frac{\frac{6!}{2!4!}\times \frac{9!}{3!6!}}{\frac{15!}{10!5!}}[/tex]
= 0.4196
Similarly,
(B)
The probability of choosing 3 liked songs = [tex]\frac{ ^6C_3\times ^9C_2}{^{15}C_5}[/tex]
[tex]=\frac{\frac{6!}{3!3!}\times \frac{9!}{2!7!}}{\frac{15!}{10!5!}}[/tex]
= 0.2398
(C)
The probability of choosing 5 liked songs = [tex]\frac{ ^6C_5\times ^9C_0}{^{15}C_5}[/tex]
[tex]=\frac{\frac{6!}{5!1!}}{\frac{15!}{5!10!}}[/tex]
≈ 0.0020
