example 1
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
a. There are 6 possible outcomes. Only 1 outcome corresponds to rolling a 5.
Number of ways to roll the dieP(rolling a 5) =
Number of ways to roll a 5
= 16
EXAMPLE 1 Find probabilities of events
b. A total of 3 outcomes correspond to rolling an even number: a 2, 4, or 6.
P(rolling even number)
=Number of ways to roll an even number
Number of ways to roll the die
= 36
12=
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.
a. 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
SOLUTION
a. There are 7! different permutations of the 7 musicians. Of these, only 1 is in alphabetical order by last name. So, the probability is:
P(alphabetical order) =17!
15040
= ≈ 0.000198
EXAMPLE 2 Use permutations or combinations
b. There are 7C2 different combinations of 2 musicians. Of these, 4C2 are 2 of your friends. So, the probability is:
P(first 2 performers are your friends) =4C2
7C2
621
=
0.286
27
=
GUIDED PRACTICE for Examples 1 and 2
You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.
1. A perfect square is chosen.
= 15
ANSWER
GUIDED PRACTICE for Examples 1 and 2
You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.
2. A factor of 30 is chosen.
= 720
ANSWER
GUIDED PRACTICE for Examples 1 and 2
What If? In Example 2, how do your answers to parts (a) and (b) change if there are 9 musicians scheduled to perform?
3.
The probability would decrease toANSWER1
362,880
The probability would decrease to 16