Question

Statistics grades: In a statistics class ofstudents, there weremen andwomen. Four of the men and five of the women received an A in the course. A student is chosen at random from the class.(a) Find the probability that the student is a woman.(b) Find the probability that the student received an A.(c) Find the probability that the student is a woman or received an A.(d) Find the probability that the student did not receive an A.

Answer 1

Answer:

(a) The probability that the student is a woman is $\frac{n_{2}}{N}$.

(b) The probability that a randomly selected student received an A is $\frac{9}{N}$.

(c) The probability that a student selected is a woman or received an A is $\frac{n_{2}+4}{N}$.

(d) The probability that a students selected did not receive an A is $\frac{N-9}{N}$.

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,

$P(M\cap A)=\frac{4}{N}$

The probability that a student is a woman and she received an A is,

$P(W\cap A)=\frac{5}{N}$

(a)

There are n₂ students in the class who are female.

The probability that the student is a woman is,

$P(W)=\frac{Number\ of\ women}{Total\ number\ of\ students}=\frac{n_{2}}{N}$

(b)

The total number of students who received an A is, 9.

The probability that a randomly selected student received an A is:

$P(A)=\frac{Number\ of\ student\ receiving\ an\ A}{Total\ number\ of\ students}=\frac{9}{N}$

(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)

                $=\frac{n_{2}}{N}+\frac{9}{N}-\frac{5}{N} \\= \frac{n_{2}+9-5}{N}\\ = \frac{n_{2}+4}{N}$

(d)

The probability that a students selected did not receive an A is:

$P(A^{c})=1-P(A)\\=1 - \frac{9}{N}\\=\frac{N-9}{N}$