Respuesta :
Answer:
(a) The probability that the student is a woman is [tex]\frac{n_{2}}{N}[/tex].
(b) The probability that a randomly selected student received an A is [tex]\frac{9}{N}[/tex].
(c) The probability that a student selected is a woman or received an A is [tex]\frac{n_{2}+4}{N}[/tex].
(d) The probability that a students selected did not receive an A is [tex]\frac{N-9}{N}[/tex].
Step-by-step explanation:
Let's assume that there were N students in a class.
Also assume that there are n₁ men and n₂ women in the class.
Let's denote M = a student is a man, W = a student is a woman and A = a student received an A in the course.
It is provided that 4 men and 5 women received an A in the course.
The probability that a student is a man and he received an A is,
[tex]P(M\cap A)=\frac{4}{N}[/tex]
The probability that a student is a woman and she received an A is,
[tex]P(W\cap A)=\frac{5}{N}[/tex]
(a)
There are n₂ students in the class who are female.
The probability that the student is a woman is,
[tex]P(W)=\frac{Number\ of\ women}{Total\ number\ of\ students}=\frac{n_{2}}{N}[/tex]
(b)
The total number of students who received an A is, 9.
The probability that a randomly selected student received an A is:
[tex]P(A)=\frac{Number\ of\ student\ receiving\ an\ A}{Total\ number\ of\ students}=\frac{9}{N}[/tex]
(c)
The probability that a student selected is a woman or received an A is:
P (W ∪ A) = P (W) + P(A) - P(W ∩ A)
[tex]=\frac{n_{2}}{N}+\frac{9}{N}-\frac{5}{N} \\= \frac{n_{2}+9-5}{N}\\ = \frac{n_{2}+4}{N}[/tex]
(d)
The probability that a students selected did not receive an A is:
[tex]P(A^{c})=1-P(A)\\=1 - \frac{9}{N}\\=\frac{N-9}{N}[/tex]
