Chapter 5.2, Problem 40E

Statistics grades: In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of the women received an A in the course. A student is chosen at random from the class.

1. Find the probability that the student is a woman.
2. Find the probability that the student received an A.
3. Find the probability that the student is a woman or received an A.
4. Find the probability that the student did not receive an A.

To determine

To find: The probability of chosen a woman from the class.

Answer to Problem 40E

The probability of chosen a woman from the class is $0.5667$

Explanation of Solution

Given information: The number of student in statistics class is $30$ ,the number of men is $13$ and the number of women is $17$ .

Calculation:

In a statistics class of $30$ students, there were $17$ women.

Hence,

  $\begin{array}{l}P(\text{Woman})=\frac{17}{30}\\ =0.5667\end{array}$

To determine

To find: The probability of the student receivedan $\text{A}$ .

Answer to Problem 40E

The probability of the student received an $\text{A}$ is $0.1667$

Explanation of Solution

Given information: The number of student in statistics class is $30$ ,the number of men is $13$ and the number of women is $17$ .

Calculation:

In a statistics class of $30$ students, two of the men and three of the women received an $\text{A}$ in the course.

The total number of students who received an $\text{A}$ in the course is,

  $2+3=5$

Hence,

  $\begin{array}{l}P(\text{Received an A})=\frac{5}{30}\\ =0.1667\end{array}$

To determine

To find: The probability of the studentis a woman orreceivedan $\text{A}$ .

Answer to Problem 40E

The probability of the student is a woman or received an $\text{A}$ is $0.6333$

Explanation of Solution

Given information: The number of student in statistics class is $30$ ,the number of men is $13$ and the number of women is $17$ .

Calculation:

In a statistics class of $30$ students, there were $17$ women. Two of the men and three of the women received an $\text{A}$ in the course.

The general addition rule for any two events $A$ and $B$ is defined as,

  $P(A\text{or}B)=P(A)+P(B)-P(A\text{and }B)$

Here,

  $\begin{array}{l}P(T\text{he student is a woman or received an A})=P(\text{Woman}\text{or}\text{Received an A})\\ \\ P(\text{Woman}\text{or}\text{Received an A})=P(\text{Woman})+P(\text{Received an A})-P\left(\begin{array}{c}\text{Woman}\text{and}\\ \text{Received an A}\end{array}\right)\end{array}$

  $\begin{array}{l}P(\text{Woman})=\frac{17}{30}\\ P(\text{Received an A})=\frac{5}{30}\\ P(\text{Woman}\text{and}\text{Received an A})=\frac{3}{30}\end{array}$

Thus,

  $\begin{array}{l}P(\text{Woman}\text{or}\text{Received an A})=\frac{17}{30}+\frac{5}{30}-\frac{3}{30}\\ =\frac{19}{30}\\ =0.6333\end{array}$

To determine

To find: The probability of the student did not receivedan $\text{A}$ .

Answer to Problem 40E

The probability of the student did not received an $\text{A}$ is $0.8333$

Explanation of Solution

Given information: The number of student in statistics class is $30$ ,the number of men is $13$ and the number of women is $17$ .

Calculation:

The rule of complements for any event $A$ is defined as,

  $P(A^c)=1-P(A)$

So,

  $\begin{array}{l}P(\text{Did not received an A}\text{})=1-P(\text{Received an A})\\ =1-\frac{5}{30}\\ =\frac{25}{30}\\ =0.83333\end{array}$