Question

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

Explanation:

Step1: Calculate the probability of William being chosen first

There are 6 students in total. The probability that William is chosen first is $\frac{1}{6}$.

Step2: Calculate the probability of Pam being chosen second

After William is chosen (1 student is already chosen), there are 5 students left. The probability that Pam is chosen second is $\frac{1}{5}$.

Step3: Calculate the combined probability

Since these are two - sequential independent events (the outcome of the first event affects the sample space of the second event), we use the multiplication rule for probabilities. The probability that William is chosen first and Pam is chosen second is $\frac{1}{6}\times\frac{1}{5}$.

$$ \frac{1}{6}\times\frac{1}{5}=\frac{1\times1}{6\times5}=\frac{1}{30} $$

Answer:

$\frac{1}{30}$