Experiment 1: A spinner has 4 equal sectors colored yellow, blue, green, and red. What is the probability of landing on purple after spinning the spinner?

Probability: It is impossible to land on purple since the spinner does not contain this color.

P(purple) | = | 0 |
= | 0 |

4 |

Experiment 2: A teacher chooses a student at random from a class of 30 girls. What is the probability that the student chosen is a girl?

Probability: Since all the students in the class are girls, the teacher is certain to choose a girl.

P(girl) | = | 30 |
= | 1 |

30 |

In the first experiment, it was not possible to land on purple. This is an example of an impossible event. In the second experiment, choosing a girl was certain to occur. This is an example of a certain event.

The next experiment will involve **a standard deck of 52 playing cards**, which consists of 4 suits: hearts, clubs, diamonds and spades. Each suit has 13 cards as follows: ace, deuce, three, four, five, six, seven, eight, nine, ten, jack, queen, and king. Picture cards include jacks, queens and kings. There are no joker cards. There are only 4 of a kind, for example, 4 tens.

Experiment 3: A single card is chosen at random from a standard deck of 52 playing cards. What is the probability that the card chosen is a joker card?

Probability: It is impossible to choose a joker card since a standard deck of cards does not contain any jokers. This is an impossible event.

P(joker) | = | 0 |
= | 0 |

52 |

Experiment 4: A single 6-sided die is rolled. What is the probability of rolling a number less than 7?

Probability: Rolling a number less than 7 is a certain event since a single die has 6 sides, numbered 1 through 6.

P(number < 7) | = | 6 |
= | 1 |

6 |

Experiment 5: A total of five cards are chosen at random from a standard deck of 52 playing cards. What is the probability of choosing 5 aces?

Probability: It is impossible to choose 5 aces since a standard deck of cards has only 4 of a kind. This is an impossible event.

P(5 aces) | = | 0 |
= | 0 |

52 |

Experiment 6: A glass jar contains 15 red marbles. If a single marble is chosen at random from the jar, what is the probability that it is red?

Probability: Choosing a red marble is certain to occur since all 15 marbles in the jar are red. This is a certain event.

P(red) | = | 15 |
= | 1 |

15 |

Summary: The probability of an event is the measure of the chance that the event will occur as a result of the experiment. The probability of an event A, symbolized by P(A), is a number between 0 and 1, inclusive, that measures the likelihood of an event in the following way:

- If P(A) > P(B) then event A is more likely to occur than event B.
- If P(A) = P(B) then events A and B are equally likely to occur.
- If event A is impossible, then P(A) = 0.
- If event A is certain, then P(A) = 1.

**Exercises**

Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1. |
A glass jar contains 5 red, 3 blue and 2 green jelly beans. If a jelly bean is chosen at random from the jar, then which of the following is an impossible event? |

2. |
A spinner has 7 equal sectors numbered 1 to 7. If you spin the spinner, then which of the following is a certain event? |

3. |
What is the probability of choosing 14 hearts from a standard deck of 52 playing cards? |

4. |
If a number is chosen at random from the following list, then what is the probability that it is prime?
2, 3, 5, 7, 11, 13, 17, 19 |

5. |
If a single 6-sided die is rolled, then which of the following events is neither certain nor impossible? |