Certain and Impossible Events
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? |