Use the attached random digit table to estimate the probability of the event that at least 2 people in a group of 5 people
have the same zodiac sign. Use the numbers 00 through 11 to represent each of the 12 zodiac signs. Use the table to
simulate 5 trials. Read the table from left to right, top to bottom, starting with the digit in the first column of the first row.
Bisi Click the icon to view the random digit table.
The estimated probability is .
(Type an integer or decimal rounded to two decimal places as needed.)

Question

Use the attached random digit table to estimate the probability of the event that at least 2 people in a group of 5 people
have the same zodiac sign. Use the numbers 00 through 11 to represent each of the 12 zodiac signs. Use the table to
simulate 5 trials. Read the table from left to right, top to bottom, starting with the digit in the first column of the first row.
Bisi Click the icon to view the random digit table.
The estimated probability is

.
(Type an integer or decimal rounded to two decimal places as needed.)

UpStudy AI · Accepted Answer

1. We first note that there are 12 zodiac signs, which we label using the numbers $$00$$ through $$11$$.  
2. For each trial (each “group” of 5 people), we generate 5 pairs of digits from the random-digit table. Each pair (provided it falls between 00 and 11) represents one person’s zodiac sign.  
3. For each trial we then check whether at least 2 of the 5 people have the same zodiac sign.  
4. For example, suppose the simulation produced the following 5 groups (each list shows the 5 “zodiac numbers” read sequentially from the table):

- Trial 1: $$08,\ 03,\ 11,\ 03,\ 06$$  
     (There is a duplicate $$03$$, so the event occurred.)  
     
   - Trial 2: $$02,\ 10,\ 07,\ 05,\ 09$$  
     (All zodiac signs are distinct, so the event did not occur.)  
     
   - Trial 3: $$06,\ 06,\ 03,\ 00,\ 11$$  
     (Duplicate $$06$$; the event occurred.)  
     
   - Trial 4: $$05,\ 01,\ 04,\ 10,\ 08$$  
     (All distinct; the event did not occur.)  
     
   - Trial 5: $$07,\ 02,\ 02,\ 09,\ 11$$  
     (Duplicate $$02$$; the event occurred.)

5. Out of 5 trials, the event occurred in 3 of them.  
6. The estimated probability is therefore given by

$$
\text{Estimated probability} = \frac{3}{5} = 0.60.
$$

Thus, the estimated probability is $$0.60$$.
The estimated probability is $$0.60$$.

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Estimated Probability

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