Question

a pair of dice was rolled 50 times and the results are in the accompanying table. from these results, calculate an empirical probability for the event “sum is less than 3 or greater than 10” (that is, 2, 11, or 12). click the icon to view the results of the experiment. according to the results of the experiment, the probability that the sum of the dice is less than 3 or greater than 10 is

Explanation:

Step1: Identify favorable outcomes

Count the number of times the sum is 2, 11, or 12 from the table. Let's assume the counts for sum = 2, sum = 11, and sum = 12 are $n_2$, $n_{11}$, and $n_{12}$ respectively. After counting from the table (not shown here but in a real - world scenario you would look at it), the total number of favorable outcomes $n=n_2 + n_{11}+n_{12}$.

Step2: Calculate empirical probability

The empirical probability $P$ is given by the formula $P=\frac{n}{N}$, where $N = 50$ (the total number of trials). So $P=\frac{n_2 + n_{11}+n_{12}}{50}$.

Answer:

$\frac{n_2 + n_{11}+n_{12}}{50}$ (where $n_2$, $n_{11}$, and $n_{12}$ are the number of times the sum of the two - dice is 2, 11, and 12 respectively as counted from the experiment results table)