Question

Twelve passengers board a train that has 5 compartments. Assuming a
random placement of passengers, find the probability that the second
compartment has one third of them.

Answer 1

Given:

Passengers that board a train= 12

Number of compartments$=5$

To Find:

The probability that the second compartment has one third of them

Step-by-step explanation:

There are $5$ compartments

passenger then each passenger can be placed in compartments in number of ways.

So, the total possible number of ways$=5^{12}$

Now for the favorable ways

we know second compartment have one third that is $4$ passenger $_{}^{12}\textrm{C}_{4}$ ways so rest $8$ passenger can be placed in

$Probability=\dfrac{favourable\ ways}{Total\ ways}$

$P=_{}^{12}\textrm{C}_{4}\times\ \dfrac{4^{8} }{5^{12}}$

$=0.133$

The probability that the second compartment has one third of them is $0.133$.