Problem 20

Explanation

First, we calculate the probability of picking two blue balls. The total number of balls in the box is the sum of yellow and blue balls.

The number of ways to choose $2$ balls from a total of $11$ balls can be calculated using combinations.

Next, we calculate the number of ways to choose $2$ blue balls from the $3$ available blue balls.

The probability of obtaining two blue balls ($P(2B)$) is the ratio of the number of ways to pick two blue balls to the total number of ways to pick any two balls.

The expected frequency ($F_h$) is the product of the probability of the event and the number of trials. The number of trials is $110$.

Thus, the expected frequency of obtaining two blue balls is $6$.