the principal uses a computer to randomly to randomly select the name of a student from all the students in the school. with the computer program, it is possible to draw the names of the same student twice. If the principal selects the name of a student from the voyagers on the first try, what is the probability she will draw the name of another student from the voyagers on the second try?
Assuming that the selection of the first student does not affect the probability of selecting any other student (i.e. the selection is done with replacement), then the probability of selecting a Voyager on the second try is also the same as the probability of selecting a Voyager on the first try, which is the proportion of Voyagers in the entire school population.
Let's say there are n students in the school, and m of them are Voyagers. Then the probability of selecting a Voyager on the first try is m/n. Since the selection is done with replacement, the probability of selecting a Voyager on the second try is also m/n (assuming the first selected student is replaced before the second draw). Therefore, the probability of drawing the name of another Voyager on the second try, given that a Voyager was selected on the first try, is:
m/n * m/n = (m/n)^2
For example, if there are 1000 students in the school and 200 of them are Voyagers, then the probability of selecting a Voyager on the second try, given that a Voyager was selected on the first try, is:
200/1000 * 200/1000 = 0.04
So there is a 4% chance of drawing the name of another Voyager on the second try, assuming that the selection process is done with replacement and is truly random.
To find the probability of the principal drawing the name of another student from the voyagers on the second try, we need to consider the number of voyagers relative to the total number of students in the school.
Let's assume there are a total of N students in the school, and M of them are voyagers.
On the first draw, the principal selects a student from the voyagers. Since there are M voyagers, the probability of choosing a voyager on the first try is M/N.
Now, on the second draw, the total number of students has decreased by 1, so there are now N-1 students remaining. However, the number of voyagers has also decreased by 1 since we've already selected one of them.
Therefore, for the principal to draw another voyager on the second try, there are M-1 voyagers left out of N-1 remaining students. Hence, the probability of the principal drawing a voyager on the second try is (M-1)/(N-1).
Therefore, the probability of the principal drawing the name of another student from the voyagers on the second try is (M-1)/(N-1).
It is important to note that this probability assumes that each student has an equal chance of being selected and that the selection on the first and second tries are independent.