Question

Half of the passengers who travel to London buy the 'Daily Boom' before boarding the train. The train is full and each compartment holds 8 passenger. What is the probability that exactly three passengers in a compartment have bought the 'Daily Boom'?

Answer 1

`21.875%`

Explanation:

We can look at this question by looking at the binomial probability general form:

`sum_(k=0)^(n)C_(n,k)(p)^k((~p)^(n-k))`

The probability that any one passenger bought a paper `(p)` is `1/2`. This means that the probability of a passenger not buying a paper `(~p)` is also `1/2`. There are 8 passengers per compartment `( :. n=8)`. We can expand the general form to show all the possibilities of paper purchases, from 0 passengers buying to all 8 buying.

We are looking specifically at 3 passengers buying the paper (and so `k=3`):

`C_(8,3)(1/2)^3(1/2)^5=((8!)/(3!5!))(1/8)(1/32)=56/(8xx32)=.21875`