Question

a die is rolled 200 times with the following results. what is the theoretical probability of the given event? ( p(3) ) a. ( \frac{1}{6} ) b. ( \frac{1}{2} ) c. 0 d. ( \frac{5}{6} )

Explanation:

Step1: Recall the formula for theoretical probability

The theoretical probability \(P(E)\) of an event \(E\) is given by \(P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).

Step2: Identify the number of favorable and total outcomes

For a fair die, the total number of possible outcomes \(n = 6\) (the numbers \(1,2,3,4,5,6\)). The number of favorable outcomes for the event \(P(3)\) is \(m = 1\) (since there is only one face with the number \(3\) on the die).

Step3: Calculate the probability

Using the formula \(P(3)=\frac{m}{n}\), we substitute \(m = 1\) and \(n=6\). So \(P(3)=\frac{1}{6}\).

Answer:

A. \(\frac{1}{6}\)