IN PYTHON

The "birthday problem" concerns the probability that in a group of people, two people

will have the same birthday. Of course, as the size of the group increases, the

probability of two people sharing the same birthday increases as well. Surprisingly, in

a

group of just 23 people, there is a 50% probability that at least two people will have

the same birthday!

The probability of two people in a group of

n

people having the same birthday may be

calculated as follows:

p(n) = 1

-

365/365 * 364/365 * 363/365 *

... * (365

-

n + 1)/365

For example, in a group of 4 people, the probability of two people having the same

birthday would be calculated as follows:

p(4) = 1

-

365/365 * 364/365 * 363/365 * (365

-

4 + 1)/365

= 1

-

365/365 * 364/365 * 363/365 * 362/365

= .016355912466550215

Requirements

Write a program named

Birthdays

.py

that prompts the user for the minimum and

maximum number of people and then outputs the probability that two people will

have the same birthday for every number between the minimum and maximum. The

probability values should be calculated using the above f

ormula, and displayed with

four decimal

places and rounded to the nearest decimal place, as shown below.

For example

(

the

red

ink highlights the user input, the

blue

ink highlights the expected

output

)

,

Minimum number of people:

4

Maximum number of peo

ple:

25

Probability of

Two People Having

Number of People the Same Birthday

----------------

-----------------

4 0.0164

5 0.0271

6 0.0405

7 0.0562

8 0.0743

9 0.0946

10 0.1169

11 0.1411

12 0.1670

13 0.1944

14 0.2231

15 0.2529

16 0.2836

17 0.3150

18 0.3469

19 0.3791

20 0.4114

21 0.4437

22 0.4757

23

0.5073

24 0.5383

25 0.5687

Design

Your

program

must prompt the user for the input values and use the method given below to

calculate each probability.

Your program

will output each probability with 4 decimal

places and

rounded to the nearest decimal place. The output must be displayed in columns as shown above.

You

should define a

calculate_probability

function and

documented as shown below:

def calculate_probability(n):

"""

Calculates probability that two people in a group of people will have the

same birthday

:param n: integer, number of people

:return: float, probability that two people will have the same birthday

"""

Implementation

Use the following named

(

constant

) variable

in your program rather than a

hard

-

wired

number

365

.

o

DAYS_PER_YEAR = 365;

Your

program

must use a loop

. The method above should be called from within the loop.

Your methods must return the correct probability value as a

double for all reasonable

input values, not just the ones used to create the table above.

Output the probability values with 4 decimal places and rounded to the last decimal place

by using a prin

t

statement to format the value. For example, the following

statement

formats an amount so that it is rounded, has 4 decimal places, and takes up a total of 20

spaces:

print("%20.4f" % 3.1415926)

You can also use the print

statement to help with formatting the number of people for each

probability value

.

Study

the code below to learn more about string formatting.

print("%10d, %10d" % (55, 777))

print("%10.4f, %10.4f" % (55.55, 0.7777777777777777))