# Probability theory problems

• Sep 23rd 2007, 07:04 PM
r7iris
Probability theory problems
1)The probability of life for any one given star in the known universe is 5.0x10^-14 independently of life for other star. Assuming that there are 100 billion galaxies in the universe and each galaxy has 300 billion stars, what is the probability of life on at least one other star in the known universe? How does this probabiliyy change if there were only a billion galaxies, each having 10 billion stars?

2) In a class there are 4 freshamn boys, 6 freshman girls and 6 sophomore boys. How many sophomore girls must be present if sex and class are to be independent when a student is selected at random?
• Sep 23rd 2007, 08:32 PM
CaptainBlack
Quote:

Originally Posted by r7iris
1)The probability of life for any one given star in the known universe is 5.0x10^-14 independently of life for other star. Assuming that there are 100 billion galaxies in the universe and each galaxy has 300 billion stars, what is the probability of life on at least one other star in the known universe? How does this probabiliyy change if there were only a billion galaxies, each having 10 billion stars?

Probability of no life for star is (1-p), where p=5.0x10^-14. Therefore the
probability of no life for any of N stars is (1-p)^N.

Therefore life for at least one of N starts is:

P=1-(1-p)^N.

In the first case N=(100 10^9)(300 10^9) = 3 10 ^22.

In the second case N=N=(1 10^9)(10 10^9) = 1 10 ^19.

Now your problem is how to evaluate P (both of these numbers
are so close to 1 to not worry about the difference).

RonL