Question

Aisha is a member of the Springfield High School swim team. Before each meet, each swimmer picks

a random lane number out of a hat.

Part A

If there are x lanes in the pool, how could you represent the probability of Aisha picking any one lane?

Show your work or explain your answer.

Enter your answer and your work or explanation in the box provided.

Part B

If there are 7 lanes, what is the probability that Aisha will draw an even numbered lane?

Answer 1

Part A:

To represent the probability of Aisha picking any one lane out of \( x \) lanes, we start by noting that the selection process is random, where each lane has an equal chance of being chosen.

The probability \( P \) of picking a specific lane can be expressed as:

\[
P(\text{picking a specific lane}) = \frac{1}{\text{total number of lanes}} = \frac{1}{x}
\]

This formula indicates that the probability of picking any one particular lane is the reciprocal of the total number of lanes \( x \).

---

Part B:

If there are 7 lanes, we need to find the probability that Aisha will draw an even-numbered lane. First, let's identify the even numbered lanes among the 7 lanes.

The even numbered lanes are 2, 4, and 6. Thus, there are a total of 3 even numbered lanes.

The total number of lanes is 7.

To find the probability of drawing an even numbered lane, we use the formula for probability:

\[
P(\text{drawing an even numbered lane}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} = \frac{\text{number of even lanes}}{\text{total number of lanes}} = \frac{3}{7}
\]

Thus, the probability that Aisha will draw an even numbered lane is:

\[
\frac{3}{7}
\]