Question

A bag contains 7 pieces of paper numbered 1 to 7. P(2)=. Is

this an experimental or theoretical probability and why?

Answer 1

`P (2) =(1)/(7)` Theoretical probability

Explanation:

The theoretical probability is defined as:

`P = (number\ of\ desired\ results)/(number\ of\ possible\ results)`

In this case we look for the probability of taking a 2 out of the bag. As there is only one paper with the number 2 in the bag then:

number of desired results = 1

The amount of paper in the bag is equal to 7, so:

number of possible results = 7

Thus:

`P (2) =(1)/(7)`

This is a theoretical probability, since we do not need to perform the experiment to calculate the probability.

To calculate the experimental probability we must perform the following experiment:

Take a paper out of the bag, record the number obtained and then return the paper to the bag.

Now repeat this experiment n times. (Perform n trials)

So:

`P (2) = (number\ of\ times\ you\ obtained\ the\ number\ 2)/(number\ of\ trials\ performed)`

To calculate a theoretical probability you always need to perform an experiment with n trials.