A history class is comprised of 7 female and 10 male students. If the instructor of the class randomly chooses 7 students from the class for an oral exam, what is the probability that 5 female students and 2 male students will be selected? Round your answer to 3 decimal places.

Respuesta :

Answer:

The probability of selecting 5 female and 2 male students is 0.052.

Step-by-step explanation:

The class comprises of 7 female students and 10 male students.

Total number of students: 17.

Number of female students, 7.

Number of male students, 10.

The probability of an event E is:

[tex]P(E)=\frac{Favorable\ outcomes}{Total\ number\ of] outcomes}[/tex]

The number of ways to select 7 students from 17 is:

[tex]N ={17\choose 7}=\frac{17!}{7!(17-7)!}= 19448[/tex]

The number of ways to select 5 female students of 7 females is:

[tex]n(F) ={7\choose 5}=\frac{7!}{5!(7-5)!}= 21[/tex]

The number of ways to select 2 male students of 10 males is:

[tex]n(M) ={10\choose 2}=\frac{10!}{2!(10-2)!}= 45[/tex]

Compute the probability of selecting 5 female and 2 male students as follows:

P (5 F and 2 M) = [n (F) × n (M)] ÷ N

                         [tex]=\frac{21\times45}{19448} \\=0.05183\\\approx0.052[/tex]

Thus, the probability of selecting 5 female and 2 male students is 0.052.

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