Luka wants to know the theoretical and experimental probability of rolling a number smaller than a 5 on a 6-sided number cube numbered 1 to 6. He rolls the number cube 10 times and records the results in this table. 1 5 2 6 4 6 2 5 6 3 Drag and drop the answers in the boxes to correctly complete the sentences comparing theoretical probability and experimental probability. actually happenedwe expect to happen231216 The theoretical probability of rolling a number smaller than 5 is because this is what. The experimental probability of rolling a number smaller than 5 is because this is what.

The experimental probability is the probability that’s we obtain from an experiment (from trials) here rolling the die and noting the number. Luka rolled ten times and 5 of these yielded a number less than 5 (the numbers on a 6-sided die that are less than five are 1, 2, 3, 4). So there were 5 out of 10 times that a number rolled was less than 5. This makes the experimental probability 5/10.

The theoretical probability is obtained through mathematical thinking (not by trying it an keeping track). On a 6-sided die there are 4 numbers less than 5. There are 6 numbers in all. Every number is equally likely to appear so the probability that a number rolled is less than 5 is 4/6. This is the theoretical probability.

As an aside, the more times you roll (100, 1000, 1000000 rolls) the closer the experimental probability (what you observe) gets to the theoretical probability (what you would expect by reasoning it out mathematically).