Question

Two mathematicians were both born in the last 500 years. Each lives (or will live) to be 100 years old, then dies. Each mathematician is equally likely to be born at any point during those 500 years. What is the probability that they were contemporaries for any length of time

Answer 1

The answer is "0.36".

Explanation:

we assume, that they are not blood-relatives, then we need both the dates (birth and death)

Births between 1512 and 2012 may occur at any time, and all of the math forms are what we have to be born at least 100 years apart.

Pr(Mathematician 1 is born inside an interval of 1512-2012 on a particular year)=
`(1)/(50000)`)

Mathematician 2 born in 1512-2012 interval on every specific year) =
`(1)/(50000)`

S Year of birth'

After that, We need to find all of the years of absolute value (birth the year Mathematician 1-birth year of Mathematician 2) <= 100 or give the probability of this happening.

Prob(Mathematician 1 birth between 1512-2012 in a specific group of 100 years):

`\to (100)/(500)=(1)/(5)`

For just a mathematician, are using the same rationale 2.

By using fact for freedom now Pr(that the dual births are divided by 100 years)) = 1-Pr(they are divided by more than 100 years):

`\to 1- ((400)/(500))^2 \\\\\to 1- ((4)/(5))^2 \\\\\to 1- (16)/(25)\\\\\to (25 -16)/(25)\\\\\to (9)/(25)\\\\\to 0.36`