Exercise 1 Page 672

We want to find a word to complete the given sentence.

A number that describes the likelihood of an event is the ___________ of an event.

The probability of an event is the measure of the likelihood of that event. The probability is a real number from 0 to 1, where 1 indicates that the event is certain to happen and 0 indicates that it is impossible. Consider that we roll a six-sided die.

Suppose that we want to know how likely it is that we roll a 3. To know this, we can find the theoretical probability or the experimental probability. To find the theoretical probability, we need to divide the number of favorable outcomes by the total number of outcomes. A six-sided die has 6 possible outcomes, and 1 of those outcomes is 3.

P( 3)= Number of Favorable Outcomes/Total Number of Outcomes

SubstituteValues

Substitute values

P( 3)= 1/6

To find the experimental probability, we need to do an experiment. Our experiment will consist of 10 trials of rolling the die. We will make a table counting the number successes of each outcome.

Outcome	Tally	Number of Successes
1	—	0
2	||	2
3	|	1
4	||	2
5	|||	3
6	||	2

We find the experimental probability dividing the number of successes by the number of trials. We can see in the table that 3 appeared 1 time. We also know that we did 10 trials. Let's find the experimental probability of rolling a 3.

P( 3)= Number of Successes/Total Number of Trials

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Substitute values

P( 3)= 1/10

We can use these probabilities to estimate the likelihood of rolling a 3. Let's complete the sentence.

A number that describes the likelihood of an event is the probability of an event.