Experimental probability

Question 1

A student rolls a standard six‑sided die 15 times. The number 3 comes up 5 times. The theoretical probability of getting a 3 on a single roll is 1/6. Which statement best explains why the experimental probability (5/15) is different from the theoretical probability?

Accepted Answer

Because only 15 rolls were made, random variation can cause the relative frequency to differ; with many more rolls the experimental probability would get closer to 1/6.

Answer

The die must be weighted toward 3 because it appeared more often than expected.

Answer

The student made a calculation error; 5/15 simplifies to 1/6.

Answer

The theoretical probability changes after each roll, so after 15 rolls the chance of a 3 becomes 1/3.

Question 2

A student flips a fair coin 20 times and records 12 heads and 8 tails. What is the experimental probability of getting a head on a single flip?

Accepted Answer

0.6

Answer

0.75

Answer

0.4

Answer

0.5

Question 3

A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. One marble is drawn at random. What is the probability that the marble drawn is blue? Express your answer as a decimal.

Accepted Answer

0.2

Answer

0.4

Answer

0.3

Answer

0.25

Try three questions

A student rolls a standard six‑sided die 15 times. The number 3 comes up 5 times. The theoretical probability of getting a 3 on a single roll is 1/6. Which statement best explains why the experimental probability (5/15) is different from the theoretical probability?

A student flips a fair coin 20 times and records 12 heads and 8 tails. What is the experimental probability of getting a head on a single flip?

A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. One marble is drawn at random. What is the probability that the marble drawn is blue? Express your answer as a decimal.

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