Concept explainers
A local fraternity is conducting a raffle where 50 tickets are to be sold—one per customer. There are three prizes to be awarded. If the four organizers of the raffle each buy one ticket, what is the
- a all of the prizes?
- b exactly two of the prizes?
- c exactly one of the prizes?
- d none of the prizes?
a.
Compute the probability that the four organizers win all of the prizes.
Answer to Problem 51E
The probability that the four organizers win all of the prizes is 0.0002.
Explanation of Solution
Probability:
For every event (say A) in sample space S, a number is called the probability of event A P(A), if it follows the following axioms.
Note that there are 3 prizes in 50 tickets. That is the number of possibilities to select 3 winners are
The number of possibilities that four organizers win all of the prizes is
The probability that the four organizers win all of the prizes is calculated as follows:
Therefore, the probability that the four organizers win all of the prizes is 0.0002.
b.
Compute the probability that the four organizers win exactly two of the prizes.
Answer to Problem 51E
The probability that the four organizers win exactly two of the prizes is 0.0141.
Explanation of Solution
The number of possibilities that four organizers win exactly two of the prizes is
The probability that the four organizers win exactly two of the prizes is calculated as follows:
Therefore, the probability that the four organizers win exactly two of the prizes is 0.0141.
c.
Compute the probability that the four organizers win exactly one of the prizes.
Answer to Problem 51E
The probability that the four organizers win exactly one of the prizes is 0.2112.
Explanation of Solution
The number of possibilities that four organizers win exactly one of the prizes is
The probability that the four organizers win exactly one of the prizes is calculated as follows:
Therefore, the probability that the four organizers win exactly one of the prizes is 0.2112.
d.
Compute the probability that the four organizers win none of the prizes.
Answer to Problem 51E
The probability that the four organizers win none of the prizes is 0.7745.
Explanation of Solution
The number of possibilities that four organizers win none of the prizes is
The probability that the four organizers win none of the prizes is calculated as follows:
Therefore, the probability that the four organizers win none of the prizes is 0.7745.
Want to see more full solutions like this?
Chapter 2 Solutions
Mathematical Statistics with Applications
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning