Theoretical vs. Experimental Probability

Question 1

What is theoretical probability?

Answer 1

Theoretical probability is the likelihood of an event occurring based on all the possible outcomes, calculated using a formula.

Question 2

How is theoretical probability expressed?

Answer 2

It is expressed as a ratio of the number of favorable outcomes to the total number of possible outcomes.

Question 3

What is experimental probability?

Answer 3

Experimental probability is the likelihood of an event occurring based on actual experiments or observations.

Question 4

How is experimental probability calculated?

Answer 4

It is calculated by taking the number of times an event occurs and dividing it by the total number of trials conducted.

Question 5

What is the formula for theoretical probability?

Answer 5

Theoretical Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)

Question 6

Can theoretical and experimental probabilities be different?

Answer 6

Yes, they can differ due to randomness or limited trials in experimental probability.

Question 7

Give an example of theoretical probability.

Answer 7

The probability of rolling a 3 on a fair six-sided die is 1/6 (one favorable outcome out of six possible outcomes).

Question 8

Give an example of experimental probability.

Answer 8

If you roll a die 60 times and roll a 3 ten times, the experimental probability of rolling a 3 is 10/60 or 1/6.

Question 9

What factors can affect experimental probability?

Answer 9

Sample size, randomness of trials, and external conditions can affect experimental probability.

Question 10

Why is it important to understand both types of probability?

Answer 10

Understanding both helps in assessing risk, making predictions, and comprehending statistical data in real-world scenarios.