Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0106
Probability is a means to measure the likelihood of the occurrence of an event. You can express probability as a real number, between 0 and 1 or as a percent. The probability of an impossible event is 0 or 0%. The probability of a certain event, which must happen, is 1 or 100%.
When you gather data by observing an event, you can calculate an experimental probability. In order to calculate experimental probability of an event use the following definition.
Example 1: |
A student flipped a coin 50 times. The coin landed on heads 28 times. Find the experimental probability of having the coin land on heads. |
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Simulation is an effective tool for finding experimental probability when conducting an actual trial is difficult. For example, if you are going to take a 6 question true-false quiz and want to know the experimental probability of guessing exactly 2 answers out of 6 correctly. You can use simulation by flipping a coin. If heads represents a correct answer, flip the coin 6 times. Then, record the number of heads. Repeat the simulation 100 times. Divide the number of times you got 2 heads by 100.
When you roll a die, the total possible outcomes are 1, 2, 3, 4, 5, and 6. The set of all possible outcomes is known as the sample space. To find a theoretical probability, find the ratio of outcomes.
| In a sample space that has n
equally likely outcomes and an event, A, occurs m of these
outcomes, then the theoretical probability of event A is
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Example 2: |
You select a number at random from the sample space {1, 2, 3, 4, 5}. Find the theoretical probability P(the number is prime). |
| Since 2, 3, and 5 are the
only prime numbers in the sample space:
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Example 3: |
Real-World Connection |
| Brown is a dominant eye color for human beings. If a father and a mother each carry a gene for brown eyes and a gene for blue eyes, what is the probability of their having a child with blue eyes? | |
| Make a table. Let B represent the dominant gene (brown eyes). Let b represent the recessive gene (blue eyes). |
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| The theoretical probability that the child will be born with brown eyes is 25%, or one in four births. | |
Sometimes you can use areas to find theoretical probability.
Example 4: |
A circular pool of radius 10 ft. is enclosed within a rectangular yard measuring 50 ft. by 100 ft. If a ball from an adjacent golf course lands at a random point within the yard, what is the probability that the ball lands in the pool? |
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| The probability that a golf ball will land in the pool is about 6.28% |
