4. Probability
Addition Rule
4:01 minutesProblem 3.3.23c
Textbook Question
23. Engineering Degrees The table shows the numbers of male and female students in the U.S. who received B.S. degrees in engineering in a recent year. A student earning a B.S. degree in engineering during that year is selected at random. Find the probability of each event.
(Source: National Center for Educational Statistics)
c. The student is not female or did not receive a mechanical engineering degree.
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected student is not female or did not receive a mechanical engineering degree. This involves using the complement rule and the addition rule in probability.
Step 2: Identify the total number of students. From the table, the total number of students who received B.S. degrees in engineering is 121,956.
Step 3: Calculate the number of students who are female and received a mechanical engineering degree. From the table, the number of females who received mechanical engineering degrees is 5,032.
Step 4: Use the complement rule to find the number of students who are not female or did not receive a mechanical engineering degree. This is equivalent to subtracting the number of students who are female and received a mechanical engineering degree from the total number of students.
Step 5: Divide the result from Step 4 by the total number of students (121,956) to find the probability. This gives the probability that a randomly selected student is not female or did not receive a mechanical engineering degree.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability
Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of selecting a student who is either not female or did not receive a mechanical engineering degree. This requires understanding how to combine probabilities of different events.
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Complementary Events
Complementary events are pairs of outcomes in a probability scenario where one event occurs if and only if the other does not. In this case, the event of selecting a student who is not female or did not receive a mechanical engineering degree can be analyzed by considering the complementary event: selecting a female student who received a mechanical engineering degree.
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Joint Probability
Joint probability refers to the probability of two events occurring simultaneously. To solve the question, one must calculate the joint probability of selecting a female student who received a mechanical engineering degree and then use this to find the probability of the complementary event. This involves using the data from the table to determine the relevant counts.
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