Answer:
(a) The probability that the student is a woman is .
(b) The probability that a randomly selected student received an <em>A</em> is .
(c) The probability that a student selected is a woman or received an <em>A</em> is .
(d) The probability that a students selected did not receive an <em>A</em> is .
Step-by-step explanation:
Let's assume that there were <em>N</em> students in a class.
Also assume that there are <em>n</em>₁ men and<em> </em><em>n</em>₂ 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 <em>A</em> in the course.
It is provided that 4 men and 5 women received an <em>A</em> in the course.
The probability that a student is a man and he received an A is,
The probability that a student is a woman and she received an A is,
(a)
There are <em>n₂</em> students in the class who are female.
The probability that the student is a woman is,
(b)
The total number of students who received an <em>A</em> is, 9.
The probability that a randomly selected student received an <em>A</em> is:
(c)
The probability that a student selected is a woman or received an <em>A</em> is:
P (W ∪ A) = P (W) + P(A) - P(W ∩ A)
(d)
The probability that a students selected did not receive an <em>A</em> is: