One hundred college seniors attending a career fair at a university were categorized according to gender and according to primary career motivation. The table below shows the results. If one of these students is to be selected at random, find the probability that the student selected is male, given that their primary motivation is a sense of giving to society.
Primary Career Motivation
Money
Allowed to be Creative
Sense of
Giving to Society
Total
Male
18
14
11
43
Female
4
21
32
57
Total
22
35
43
100
To find the probability that the student selected is male, given that their primary motivation is a sense of giving to society, we need to look at the table and find the intersection of the "Sense of Giving to Society" row and the "Male" column.
The number in the intersection of these categories is 11.
The total number of students with a primary motivation of a sense of giving to society is 43.
To find the probability, we divide the number of students in the intersection by the total number of students in the "Sense of Giving to Society" row:
P(Male | Sense of Giving to Society) = 11/43 ≈ 0.26
Therefore, the probability that the student selected is male, given that their primary motivation is a sense of giving to society, is approximately 0.26.
To find the probability that a student selected at random is male, given that their primary motivation is a sense of giving to society, we need to calculate the conditional probability.
Conditional probability is defined as the probability of an event happening given that another event has already occurred. In this case, the event we are interested in is selecting a male student, and the event that has already occurred is that their primary motivation is a sense of giving to society.
To calculate the conditional probability, we need to divide the number of favorable outcomes (male students with a sense of giving to society) by the total number of outcomes (all students with a sense of giving to society).
According to the table, the number of male students with a sense of giving to society is 11.
The total number of students with a sense of giving to society (regardless of gender) is 43.
Therefore, the probability that the student selected is male, given that their primary motivation is a sense of giving to society is:
P(Male|Sense of Giving to Society) = Number of Male students with a sense of giving to society / Total number of students with a sense of giving to society
= 11 / 43
The probability is approximately 0.256 (rounded to three decimal places).
So, the probability that the student selected is male, given that their primary motivation is a sense of giving to society, is approximately 0.256.
To find the probability that a randomly selected student is male, given that their primary motivation is a sense of giving to society, we need to use conditional probability.
First, we need to identify the total number of students whose primary motivation is a sense of giving to society. According to the table, there are 43 students whose primary motivation is a sense of giving to society.
Next, we need to find the number of those students who are male. According to the table, there are 11 male students whose primary motivation is a sense of giving to society.
The probability of selecting a male student, given that their primary motivation is a sense of giving to society, is calculated by dividing the number of male students with a sense of giving to society by the total number of students with a sense of giving to society:
P(Male | Sense of Giving to Society) = Number of Male Students with a Sense of Giving to Society / Total Number of Students with a Sense of Giving to Society
P(Male | Sense of Giving to Society) = 11 / 43
Therefore, the probability that a randomly selected student is male, given that their primary motivation is a sense of giving to society, is 11/43.