# Thread: Probability of a birthday being on a Monday for 3750 people

1. ## Probability of a birthday being on a Monday for 3750 people

A firm employs 3750 people.
One person is chosen at random. What is the probability that the persons birthday is on a Monday in the year 2008. Write the answer as a decimal to two d.p.

Attempt ONE

There are 52 Monday's in 1 year so I did 52/3750 = 0.014 WRONG ANSWER

Many attempts later
Thinking that there are 52 Monday's in 365 days I did 52/365 = 0.14 because this is the probability of there being a Monday in 1 year. CORRECT ANSWER

BUT I'm not happy. I just got the answer by not really knowing what I'm doing. Why did I not need to use the 3750 people value?

What happens if the question asked about the probability of TWO people's birthday being on a Monday?
Would the answer be (52/365)×(52/365) = 0.02?

2. Yes, the number of people working at the company is just a red herring. Math exercises love to include completely irrelevant information to lead you astray, so as to better prepare you for real world scenarios which are often chock-full of red herrings. For this problem, all that matters is that you pick one person at random from the company. For all intents and purposes, which day of the year a person is born on is completely random. In a more realistic exercise, you might have considered birth rates and holidays and what not to determine the "hot spots" for more births than typical, but that's not needed here...

The second method is correct because any individual person, picked at random, has a 1/365 chance of being born in any given day. Since there are 52 Mondays in 2008, that gives a 52/366 (because 2008 was a leap year) chance of that person being born on a Monday. Because of the error introduced by rounding to two decimal places, 1/7 would have also been an acceptable answer, since there's only seven possible days to choose from. 52/366 is slightly more accurate because that accounts for the fact that some weekdays appear slightly more often than others do in a given calendar year.

Your proposed answer for the scenario in which two people are picked at random is also correct. What day of the week a person is born on is an independent event. One person being born on, say, a Thursday, in no way affects the chance of the other person being born on Monday.

4. Now think about these three scenarios:

A firm employs 3750 people.
One person is chosen at random. What is the probability that only that persons birthday is on a Monday in the year 2008. Write the answer as a decimal to two d.p

A firm employs 3750 people.
two persons are chosen at random. What is the probability that only those two persons birthday is on a Monday in the year 2008. Write the answer as a decimal to two d.p

A firm employs 3750 people.
What is the probability that there are at least two persons birthday is on a Monday in the year 2008. Write the answer as a decimal to two d.p

5. Originally Posted by Subhotosh Khan
Now think about these three scenarios:

A firm employs 3750 people.
One person is chosen at random. What is the probability that only that [COLOR=#333333]persons birthday is on a Monday in the year 2008. Write the answer as a decimal to two d.p

(1/3750).(52/365) = 0.000037

6. Originally Posted by Subhotosh Khan

[/COLOR]A firm employs 3750 people.
two persons are chosen at random. What is the probability that only those two [COLOR=#333333]persons birthday is on a Monday in the year 2008. Write the answer as a decimal to two d.p
(1/3750).(1/3750).(52/365) = 1.01x10 to the power MINUS 8

For the last question it 1 minus that value

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