Respuesta :
Answer:
0.353
Step-by-step explanation:
We have been given that a history class is comprised of 7 female and 10 male students.
We will use combinations to solve our problem.
We can choose 6 female students out of 7 female students in [tex]_{6}^{7}\textrm{C}[/tex] ways.
[tex]_{6}^{7}\textrm{C}=\frac{7!}{(7-6)!6!} =\frac{7*6!}{1!6!} =7[/tex]
We can choose 7 male students out of 10 male students in [tex]_{7}^{10}\textrm{C}[/tex] ways.
[tex]_{7}^{10}\textrm{C}=\frac{10!}{(10-7)!7!} =\frac{10!}{3!7!} =\frac{10*9*8*7!}{3*2*1*7!}= 5*3*8=120[/tex]
So the number of ways that 6 female and 7 males can be chose is: 7*120 = 840.
Now let us find ways in which 13 students can be chosen from 17 students as: [tex]_{13}^{17}\textrm{C}[/tex]
[tex]_{13}^{17}\textrm{C}=\frac{17!}{(17-13)!13!}=\frac{17!}{4!13!} =\frac{17*16*15*14*13!}{4*3*2*1*13!} =17*4*5*7=2380 [/tex]
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
Now let us substitute our values in probability formula.
[tex]P(\text{6 female and 7 males})=\frac{840}{2380}[/tex]
[tex]P(\text{6 female and 7 males})= 0.3529411764705882\approx 0.353[/tex]
Therefore, the probability of selecting 6 female students and 7 male students is 0.353.
