Question

this past semester, a professor had a small business calculus section. the students in the class were dave, jenia, pam, william, allison, a, kristin, and veda. suppose the professor randomly selects two people to go to the board to work problems. what is the probability that pam is the first person chosen to go to the board and dave is the second? p(pam is chosen first and dave is second) = (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of students

There are 8 students in total.

Step2: Calculate probability of Pam being first

The probability that Pam is chosen first is $\frac{1}{8}$ since there is 1 Pam out of 8 students.

Step3: Calculate probability of Dave being second given Pam was first

After Pam is chosen first, there are 7 students left. The probability that Dave is chosen second is $\frac{1}{7}$.

Step4: Calculate joint - probability

By the multiplication rule for independent events in a sequence, the probability that Pam is first and Dave is second is $\frac{1}{8}\times\frac{1}{7}=\frac{1}{56}$.

Answer:

$\frac{1}{56}$