Concept explainers
(a)..
To find: The way in which the given pattern gives the possibility that the
(a)..
Answer to Problem 67E
The given statement is False.
Explanation of Solution
Given:
The given pattern is,
Also,
Calculation:
Consider for
Consider for
Thus, the two pattern shows that the
(b)..
To find: The probability that
(b)..
Answer to Problem 67E
The probability is
Explanation of Solution
Calculation:
Consider the given pattern is,
Also,
Consider the pattern for
(c)..
To prove: The probability for the n number of people is
(c)..
Explanation of Solution
Given:
The recursive equation to determine the probability is,
Calculation:
Consider the probability that 2 people have distinct birthday is,
Consider the probability that 3 people have distinct birthday is,
Consider the probability that 4 people have distinct birthday is,
Thus, the probability for the n people is,
Hence, proved.
(d)..
To find: The way in which the given expression gives the probability that at least two people in a group of n people have the same birthday.
(d)..
Answer to Problem 67E
The probability that at least two person have the birthday is
Explanation of Solution
Given:
The given equation is,
Calculation:
Consider the person with the probability of birthday
Thus, the probability that at least two person have the birthday is,
(e)..
To find: The completed form of the given table.
(e)..
Answer to Problem 67E
The completed table is shown in Table 2..
Explanation of Solution
Given:
The given table is shown in Table 1
Table 1
10 | 15 | 20 | 23 | 30 | 40 | 50 | |
Calculation:
Consider the formula for the probability of n people is,
Consider the formula to calculate the probability that at least two people have same birthday is,
Then, the completed table is shown in Table 2
Table 2
10 | 15 | 20 | 23 | 30 | 40 | 50 | |
0.88 | 0.75 | 0.59 | 0.49 | 0.29 | 0.11 | 0.03 | |
0.12 | 0.25 | 0.45 | 0.51 | 0.71 | 0.89 | 0.97 |
(f)..
To find: The number of people that must be there so that the probability of at least two of the man having same birthday is more than
(f)..
Answer to Problem 67E
The number of people in the group must be 23.
Explanation of Solution
Consider the formula to calculate the probability that at least two people have same birthday is,
From the table 2.
SO, the number of people in the group must be 23.
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
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