Probability

Probability is a measure of the likelihood of an event occurring. All probabilities range from 0 to 1, where 0 is the probability of an event that cannot happen and 1 is the probability of an event that is certain to happen. An event with probability 0.5, or 50%, has an equal chance of happening or not happening.

The formula P ( E ) = number of favorable outcomes number of possible outcomes p open e close equals . fraction numberoffavorableoutcomes , over numberofpossibleoutcomes end fraction  is used to calculate the probability of event E.

Example 1

The numbers 2 through 21 are written on pieces of paper and placed in a hat. One piece of paper is drawn at random. Determine the probability of selecting a perfect square.

The total number of outcomes, 2 , 3 , 4 , ⋯ , 21 , 2 comma 3 comma 4 comma math axis ellipsis comma 21 comma  for this event is 20.

There are 3 favorable outcomes: 4, 9, and 16.

P ( selecting a perfect square ) = 3 20 p open . selectingaperfectsquare . close equals , 3 twentieths

Example 2

Determine the probability of getting exactly two heads when two coins are tossed.

The total number of outcomes, (H, H), (H, T), (T, H), (T, T), for this event is 4.

There is 1 favorable outcome, (H, H).

P ( two heads ) = 1 4 p open . twoheads . close equals . 1 fourth

Exercises

A jar contains 3 white balls, 7 red balls, and 4 green balls. A ball is selected at random from the jar. Determine each probability.

1. P(red)
2. P(white)
3. P(green)
4. P(green or white)
5. A red ball is removed from the jar. What is the probability that the next ball selected will be green?

You roll a 12-sided number cube. Determine each probability.

6. P(2)
7. P(4 or 5)
8. P(even number)
9. P(odd number)
10. P(prime number)
11. P(factor of 8)

A coin is flipped three times. Determine the probability of each outcome.

12. exactly two tails
13. two heads and one tail
14. no more than two tails
15. no more than one head
16. at least one tail
17. all tails or all heads

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