of the 30 students in the sixth period math class, 8 are also in the same fourth period science class. which…

of the 30 students in the sixth period math class, 8 are also in the same fourth period science class. which can be used to determine the probability that if three students are chosen at random from the math class to do a group project, the first student chosen to be in the group is in the fourth period science class but the other two are not?\n(8/30)(22/29)(21/28)\n(8/30)(8/30)(8/30)\n(8/30)(7/29)(6/28)\n(8/30)(22/30)(21/30)

of the 30 students in the sixth period math class, 8 are also in the same fourth period science class. which can be used to determine the probability that if three students are chosen at random from the math class to do a group project, the first student chosen to be in the group is in the fourth period science class but the other two are not?\n(8/30)(22/29)(21/28)\n(8/30)(8/30)(8/30)\n(8/30)(7/29)(6/28)\n(8/30)(22/30)(21/30)

Answer

Explanation:

Step1: Probability of first - student

The probability that the first student chosen is from the fourth - period science class is the number of students in both classes divided by the total number of students in the math class. There are 8 students in both classes and 30 students in the math class, so the probability is $\frac{8}{30}$.

Step2: Probability of second - student

After choosing one student from the fourth - period science class, there are 29 students left in the math class. The number of students not in the fourth - period science class is $30 - 8=22$. So the probability that the second student is not from the fourth - period science class is $\frac{22}{29}$.

Step3: Probability of third - student

After choosing two students, there are 28 students left. After choosing one from the fourth - period science class and one not from it, there are 21 students left who are not from the fourth - period science class. So the probability that the third student is not from the fourth - period science class is $\frac{21}{28}$.

Step4: Combined probability

By the multiplication rule of probability for dependent events, the probability that the first student is from the fourth - period science class and the other two are not is the product of the probabilities of each step, which is $\left(\frac{8}{30}\right)\left(\frac{22}{29}\right)\left(\frac{21}{28}\right)$.

Answer:

$\left(\frac{8}{30}\right)\left(\frac{22}{29}\right)\left(\frac{21}{28}\right)$