The CSU system reported the following probabilities for their student body in 2013. The probability of their student being a male between 17 and 19 is P(A) = 0.11. The probability of their student being a female between 20 and 24, P(B) = 0.30. What is P(A and B) given that year? 0.033 0.410 0.377 0
Question
The CSU system reported the following probabilities for their student body in 2013. The probability of their student being a male between 17 and 19 is P(A) = 0.11. The probability of their student being a female between 20 and 24, P(B) = 0.30. What is P(A and B) given that year? 0.033 0.410 0.377 0
Solution 1
The probability of events A and B occurring simultaneously, denoted as P(A and B), refers to the likelihood of both events happening at the same time. In this case, event A is a student being a male between 17 and 19, and event B is a student being a female between 20 and 24.
However, these two events are mutually exclusive, meaning they cannot occur at the same time. A student cannot be both a male between 17 and 19 and a female between 20 and 24 at the same time. Therefore, the probability of both events occurring simultaneously, P(A and B), is 0.
Solution 2
The probability of events A and B occurring simultaneously, denoted as P(A and B), refers to the likelihood of both events happening at the same time. However, in this case, events A and B are mutually exclusive - meaning they cannot occur at the same time.
Event A is a student being a male between 17 and 19, and event B is a student being a female between 20 and 24. A student cannot be both a male between 17 and 19 and a female between 20 and 24 at the same time.
Therefore, P(A and B) = 0. This is because the intersection of these two events is empty - there is no overlap between them. So, the correct answer is 0.
Similar Questions
An engineering school reports that 55% of its students were male (M), 40% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20.What is the probability of a random student being a female who is not between the ages of 18 and 20? 0.27 0.25 0.30 0.45
A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 15 7 14 36Female 11 5 2 18Total 26 12 16 54If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got a 'B'.
The gender and year of each of the 191 students in a high school band were recorded. The data are summarized in the table below.Freshman Sophomore Junior SeniorMale 30 14 21 18Female 42 22 17 27Suppose a student from the high school band is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a) What is the probability that the student is female or a freshman?(b) What is the probability that the student is male, given that the student is a sophomore?
In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student has an A given that the student is female?Female MaleHas an A 15 3Does not have an A 2 8
In a certain liberal arts college with about 10,000 students, 40% are males. If two students from this college are selected at random, what is the probability that they are both males? 0 0.16 0.80 0.64 0.25
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.