Problem

A die is rolled 50 times with the following results. \begin{tabular}{r|rrrrrr} Outcome & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 9 & 8 & 5 & 7 & 19 & 2 \end{tabular} Compute the empirical probability that the die comes up a 5. A. $\frac{21}{100}$ B. $\frac{1}{3}$ C. $\frac{19}{50}$ D. $\frac{1}{6}$

Solution

Step 1 :A die is rolled 50 times with the following results: Outcome: 1, 2, 3, 4, 5, 6 Frequency: 9, 8, 5, 7, 19, 2

Step 2 :We are asked to compute the empirical probability that the die comes up a 5.

Step 3 :The empirical probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.

Step 4 :In this case, the event is the die coming up a 5, which occurred 19 times.

Step 5 :The total number of trials is the total number of times the die was rolled, which is 50.

Step 6 :So, the empirical probability is \(\frac{19}{50}\).

Step 7 :Final Answer: The empirical probability that the die comes up a 5 is \(\boxed{\frac{19}{50}}\).

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Source: https://solvelyapp.com/problems/FVDfw8gUKs/

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