Question

1. if the empirical probability of rolling a 2 on a die is $\frac{4}{25}$, how many times did the number 2 appear in 25 rolls?

a. 3
b. 4
c. 5
d. 6

Explanation:

Step1: Recall the formula for empirical probability

Empirical probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Let \(x\) be the number of times \(2\) appears. We know \(P = \frac{4}{25}\) and total number of outcomes \(n = 25\).

Step2: Substitute into the formula

Using \(P=\frac{x}{n}\), substitute \(P=\frac{4}{25}\) and \(n = 25\). So \(\frac{4}{25}=\frac{x}{25}\).

Step3: Solve for \(x\)

Cross - multiply: \(25x=4\times25\). Divide both sides by \(25\), \(x = 4\).

Answer:

B. 4