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EXAMPLE 1

There are 6 possible outcomes. Only 1 outcome corresponds to rolling a 5. Number of ways to roll a 5. P ( rolling a 5). =. Number of ways to roll the die. 1. =. 6. EXAMPLE 1. Find probabilities of events.

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EXAMPLE 1

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  1. There are6possible outcomes. Only 1outcome corresponds to rolling a 5. Number of ways to roll a 5 P(rolling a5) = Number of ways to roll the die 1 = 6 EXAMPLE 1 Find probabilities of events You roll a standard six-sided die. Find the probability of (a) rolling a 5 and (b) rolling an even number. SOLUTION

  2. A total of 3outcomes correspond to rolling an even number: a 2, 4, or 6. Number of ways to roll an even number = Number of ways to roll the die 3 1 = 6 2 = EXAMPLE 1 Find probabilities of events P(rolling even number)

  3. What is the probability that the musicians perform in alphabetical order by their last names? (Assume that no two musicians have the same last name.) EXAMPLE 2 Use permutations or combinations Entertainment A community center hosts a talent contest for local musicians. On a given evening, 7 musicians are scheduled to perform. The order in which the musicians perform is randomly selected during the show.

  4. There are 7! different permutations of the 7musicians. Of these, only 1is in alphabetical order by last name. So, the probability is: 1 P(alphabetical order) 1 = 7! = 5040 EXAMPLE 2 Use permutations or combinations SOLUTION ≈ 0.000198

  5. There are 7C2different combinations of 2 musicians. Of these, 4C2are 2 of your friends. So, the probability is: 4C2 P(first2performers are your friends) = 7C2 6 2 = = 21 7 0.286 EXAMPLE 2 Use permutations or combinations

  6. A perfect square is chosen. 1 ANSWER = 5 for Examples 1 and 2 GUIDED PRACTICE You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.

  7. A factor of 30 is chosen. 7 ANSWER = 20 for Examples 1 and 2 GUIDED PRACTICE You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.

  8. What If?In Example 2, how do your answers to parts (a) and (b) change if there are 9 musicians scheduled to perform? The probability would decrease to 1 1 6 The probability would decrease to ANSWER 362,880 for Examples 1 and 2 GUIDED PRACTICE

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