Explanation Given: The faculty of the mathematics department at Joliet Junior College is composed of 4 females and 9 males. Of the 4 females, 2 are under age 40, and of the 9 males, 3 are under age 40. Formula Used: P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) Calculation: Total number of faculties = 9 + 4 = 13 . a. N u m b e r o f f e m a l e = 4 . N u m b e r o f f a c u l t y u n d e r a g e 40 = 2 + 3 = 5 . P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A To determine To find: The probability that a randomly selected faculty member is:

Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)

4th Edition

ISBN: 9780137399635

Author: Michael Sullivan, Michael Sullivan

Publisher: PEARSON+

See similar textbooks

Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

Videos

Question

Chapter 12.3, Problem 70AYU

To determine

To find: The probability that a randomly selected faculty member is:

a. Female or under age 40.

To determine

To find: The probability that a randomly selected faculty member is:

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 69AYU

Chapter 12.3, Problem 71AYU

Students have asked these similar questions

1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps (each step must be justified). Theorem 0.1 (Abel's Theorem). If y1 and y2 are solutions of the differential equation y" + p(t) y′ + q(t) y = 0, where p and q are continuous on an open interval, then the Wronskian is given by W (¥1, v2)(t) = c exp(− [p(t) dt), where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or W (y1, y2)(t) = 0 for every t in I. 1. (a) From the two equations (which follow from the hypotheses), show that y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0, 2. (b) Observe that Hence, conclude that (YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0. W'(y1, y2)(t) = yY2 - Y1 y2- W' + p(t) W = 0. 3. (c) Use the result from the previous step to complete the proof of the theorem.

2. Observations on the Wronskian. Suppose the functions y₁ and y2 are solutions to the differential equation p(x)y" + q(x)y' + r(x) y = 0 on an open interval I. 1. (a) Prove that if y₁ and y2 both vanish at the same point in I, then y₁ and y2 cannot form a fundamental set of solutions. 2. (b) Prove that if y₁ and y2 both attain a maximum or minimum at the same point in I, then y₁ and Y2 cannot form a fundamental set of solutions. 3. (c) show that the functions & and t² are linearly independent on the interval (−1, 1). Verify that both are solutions to the differential equation t² y″ – 2ty' + 2y = 0. Then justify why this does not contradict Abel's theorem. 4. (d) What can you conclude about the possibility that t and t² are solutions to the differential equation y" + q(x) y′ + r(x)y = 0?

Question 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2-t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = 1+t, y = 2 − t, z = 4 - 3t and is parallel to the plane 5x + 2y + z = 1. (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y = 1+t, and z = 2-t. (e) The plane that contains the lines L₁: x = 1 + t, y = 1 − t, z = 2t and L2 : x = 2 − s, y = s, z = 2.

Chapter 12 Solutions

Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)

Ch. 12.1 - Prob. 1AYU Ch. 12.1 - Prob. 2AYU Ch. 12.1 - Prob. 3AYU Ch. 12.1 - Prob. 4AYU Ch. 12.1 - Prob. 5AYU Ch. 12.1 - Prob. 6AYU Ch. 12.1 - Prob. 7AYU Ch. 12.1 - Prob. 8AYU Ch. 12.1 - Prob. 9AYU Ch. 12.1 - Prob. 10AYU

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The probability that a randomly selected faculty member is: a. Female or under age 40.

Solution Summary: The author explains that the mathematics department at Joliet Junior College is composed of 4 females and 9 males.