Question

answer so a middle schooler could understand and break it down
(a)
In analyzing a baseball team’s performance over several seasons, the coach ​observed that a particular baseball player hit a home run once every 10
​times at bat.
​
​Part A
Explain a procedure for using a random number generator to ​simulate the baseball player’s hitting outcome as either a homerun or ​not a homerun assuming the pattern continues as described above.
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(b)

​
​Part B
Based on the procedure given in Part A, what is one possible ​simulation result that represents the player hitting 2
consecutive
​homeruns during 10
times at bat?

Answer 1

I'll keep this simple and step-by-step.

Part A — Procedure to simulate each at-bat
1. Know the chance: the player hits a home run (HR) 1 out of 10 times, so the probability is 1/10 = 0.1.
2. Decide how to use the random number generator:
- Option A (easiest): Generate a random digit from 0 to 9. Let 0 = home run and 1–9 = not a home run.
- Option B: If your generator gives a random decimal between 0 and 1, treat any number ≤ 0.1 as a home run and any number > 0.1 as not a home run.
3. Repeat the random draw for each at-bat. Each draw is one at-bat and they are independent (what happens in one at-bat doesn’t change the others).
4. Record H for home run or N for not a home run for each of the 10 draws.

Part B — One possible simulation result showing 2 consecutive home runs
Using Option A (0 = HR, 1–9 = not), suppose the 10 random digits you get are:
4, 7, 0, 0, 9, 3, 2, 1, 6, 8

Convert each digit to H or N:
N, N, H, H, N, N, N, N, N, N

This result shows two consecutive home runs (H, H) on the 3rd and 4th at-bats.