# 2.1.3 - Probability Rules

The probability rules covered in this lesson can be found in section P.1 of the Lock5 textbook.

Earlier in this lesson you were introduced to proportions. We used the notation: $$Proportion=\frac{Number\;in\;the\;category}{Total\;number}$$.

When we discuss probabilities, we will use the notation below where $$P(A)$$ is the probability of event $$A$$ occurring. Probabilities are typically written in decimal form but may also be translated to percentages.

Note that this is the same formula that you learned earlier in Lesson 2.1.1 for a proportion.

Probability of Event A
$$P(A)=\dfrac{Number\;in\;group\;A}{Total\;number}$$

What is the probability that a randomly selected card from a standard 52-card deck will be a spade? There are 13 spades in the deck of 52.

$$P(spade)=\dfrac{13}{52}=0.25$$

The probability of pulling a spade is 0.25. We could also say that there is a 25% chance of pulling a spade.

## Example: Odd Numbers Section

If you roll a six-sided die, what is the probability of getting an odd number? There are three odd numbers on the die (1, 3, 5).

$$P(odd)=\dfrac{3}{6}=0.50$$

The probability of rolling an odd number is 0.50. We could also say that there 50% chance of rolling an odd number.

## Example: Raffle Section

There are a total of 500 raffle tickets and you have purchased 10. What is the probability that one of your tickets will be randomly selected to win the raffle?

$$P(winning)=\dfrac{10}{500}=0.02$$

The probability of you winning is 0.02. We could also say that there is a 2% chance that you will win.