Prove that if a σ-algebra of subsets of r contains intervals of the form (a,[infinity]), then it contains all the intervals.

Asix-sided die of unknown bias is rolled 20 times, and the number 3 comes up 6 times. in the next three rounds (the die is rolled 20 times in each round), the number 3 comes up 6 times, 5 times, and 7 times. the experimental probability of rolling a 3 is 10 %, which is approximately % more than its theoretical probability. (round off your answers to the nearest integer.)