Birthdays

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Binomial Probability

HAPPY BIRTHDAYS

The Birthday applet above simulates birthdays of various sized groups.
Type into the box the number of people in your group, up to 100 maximum, and press the Enter key.
The applet assigns a birthday to each person in the group.
Birthdays displayed in red are duplicates.
The 100 Counter increments each time you press the ENTER key in the People box.
The 100 Counter counts up to 100 randomly chosen groups of the size entered in the People box.
The Same Birthdays counter increments each time a group contains duplicate birthdays.
You can compare your results in the mathlet above to your entries in the table below.
This is how statisticians test their data and formulas against each other.
It's a way of checking inductions against deductions.

DIRECTIONS

The table below requires you to use complementary probabilities to compute the chances that at least two people share the same birthday within a group of people of a given size.
In the table, column n represents groups ranging from 1 to 30 people.
In the CHOICES column, enter the number of birthdays the nth person may have so that it will NOT match the birthday of anyone else in the group.
In the CHANCES column, enter the probability that there will be NO matches among this number of people.
Remember: probability is the number of events you want divided by the total number of events possible.
The CHANCES column must be correct to the nearest thousandths ( .001 ) . That's 3 decimal places.
In a group of size 1, the lone individual may have any birthday.
The chance that the lone individual's birthday differs from someone else in the group is 1, because there is no one else in the group!
But in a group of size 2, how many birthdays may the second person have that differ from the first person's?
Use this number to calculate the chance that the second person's birthday differs from the first.
Continue in this manner till you have filled out the table.
Ignore leap years.
What do the numbers in Column 3 and Column 4 represent?
Do your calculations approximate the results in the simulation above?

After completing this table, screencopy and email it to your instructor.
Use the completed table to answer the questions in the table below.
Screencopy and email your answers to these questions also.
Show your calculations.

QUESTIONS

What do we call the type of probability in Column 3?
What do we call the type of probability in Column 4?
What is the probability that two randomly selected people will NOT have the same birthday?
What is the probability that two randomly selected people will have the same birthday?
What is the probability that three randomly selected people will NOT have the same birthday?
What is the probability that three randomly selected people will have the same birthday?
What is the probability that no two people in our class have the same birthday? Assume there are now 15 members left in our class.
What is the probability that at least one member of our class has the same birthday as another?
Run the birthday simulation above 100 times for groups of 15 people.
How many groups had at least one duplicate birthday?
Run your own simulation. Do not copy the numbers from someone else.
How many people must be in a classroom so the chance that two of them have the same birthday is roughly 50%?
How many people must be in a classroom so the chance that two of them have the same birthday is 100%?
What is the probability that at least 2 out of 3 randomly selected people were born on the same day of the week?
Assuming there are twelve equally likely zodiac signs, what is the probability that at least 2 out of 3 randomly selected people have the same zodiac sign?
If three dodecahedron dice are rolled, what is the probability that at least two of them land with the same number showing on top?

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Last Modified 11/5/08 8:02 AM