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This past semester, a professor had a small business calculus section. The students in the class were Jinita, Neta, Kristin, Mike, and Dave. Suppose the professor randomly selects two people to go to the board to work problems. What is the probability that Neta is the first person chosen to go to the board and Mike is the second?

P(Neta is chosen first and Mike is second): (Type an integer or a simplified fraction.)

Sagot :

GinnyAnsweridn
To solve this problem, we start by considering the total number of students in the class, which is 5. We are interested in the probability of selecting Neta first and then Mike second.

Step 1: Probability of selecting Neta first

Since there are 5 students, the probability of selecting Neta as the first person is:
[tex]\[ \frac{1}{5} \][/tex]

Step 2: Probability of selecting Mike second

After selecting Neta, there are 4 students remaining. The probability of selecting Mike from these remaining 4 students is:
[tex]\[ \frac{1}{4} \][/tex]

Step 3: Combined Probability

To find the probability that Neta is chosen first and Mike is chosen second, we multiply the probabilities from Step 1 and Step 2:
[tex]\[ \frac{1}{5} \times \frac{1}{4} = \frac{1}{20} \][/tex]

So, the probability that Neta is the first person chosen and Mike is the second person chosen is:
[tex]\[ \frac{1}{20} \][/tex]

Thus, the probability is [tex]\( \frac{1}{20} \)[/tex], or 0.05 as a decimal.
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