Im not sure how to start here. Please help.
The age distribution of students at a community college is given below.
Age (years)
Under 21
21-25
26-30
31-35
Over 35
Number of students (f)
411
407
201
51
26
A student from the community college is selected at random. Find the conditional probability that the student is between 26 and 30 given that he or she is at least 26.
Of the 278 (201+51+26) students who are 26 or older, 201 are 26-30. That is a probability of 206/278 = 74.1%
I'm not sure I understand this. Why are we including 51, and 26 if there are only 201 students that are between 26-30. Where does 206 come from?
To find the conditional probability that the student is between 26 and 30 given that he or she is at least 26, we need to consider the total number of students who are at least 26 and calculate how many of them fall into the age range of 26-30.
In this case, the age distribution table shows that there are 411 students under 21, 407 students aged 21-25, 201 students aged 26-30, 51 students aged 31-35, and 26 students over 35.
To calculate the probability, we need to focus on the students who are at least 26, which includes students aged 26, 27, 28, 29, 30, 31, 32, 33, 34, and 35+.
Out of these students, we need to determine how many fall into the age range of 26-30. From the table, we see that there are 201 students in this age range.
Therefore, to find the conditional probability, we divide the number of students aged 26-30 (201) by the total number of students who are at least 26 (which includes ages 26-30, 31-35, and over 35).
The total number of students aged 26 or older is obtained by summing up the frequencies for ages 26-30, 31-35, and over 35, which is 201 + 51 + 26 = 278.
So, the probability of a student being between 26 and 30, given that they are at least 26, is 201/278, which is approximately 0.741 or 74.1%.
The value of 206 you mentioned is not directly related to this probability calculation. It seems to be a typographical error. The correct probability is indeed 201/278.