Concept explainers
a.
Find the probabilities that the
a.
Answer to Problem 67E
The pattern gives the probabilities that
Explanation of Solution
Calculation:
Let us consider that a room is filled with
If we consider
If we consider
Hence, the pattern gives the probabilities that
b.
Write an expression for the probability.
b.
Answer to Problem 67E
Explanation of Solution
Calculation:
If we use the pattern in (a), then probability that
c.
Verify that this probability can be obtained recursively.
c.
Answer to Problem 67E
Explanation of Solution
Calculation:
The probability that at least two people share the same birthday is the complement of the probability that no two people have the same birthday
Probability that
Probability that
Probability that
Hence probability that
If
d.
Find the probability that at least two people in a group of
d.
Answer to Problem 67E
Explanation of Solution
Calculation:
Let us try to find the probability that at least one person has the same birthday as you.
This will determine the probability that at least two people have the same birthday
An individual person will not have the same birthday as you with probability
Hence the probability that n people all do not have your birthday is then
So the probability that at least one person does have your birthday, or
Probability that at least two people have the same birthday is given by
e.
Complete the table.
e.
Answer to Problem 67E
Explanation of Solution
Calculation:
Let us put various values of
Since
We know that
Similarly, we can calculate for all values for n from 1 to 50
Now,
We have already calculated requires values for
We can easily calculate requires values for
Hence,
Similarly, all required values can be calculated for different values of n from 1 to 50
Hence, we get the following answers after calculating for various values of n
f.
Find the probability.
f.
Answer to Problem 67E
Explanation of Solution
Calculation:
Let us try to find how many people must be there in a group for a specific condition
From (d), we know that probability of at least two people having same birthday is given by
Also, from the table derives in (e) above, we see that for
Hence, there must be
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning