Answer to Question #211823 in Quantum Mechanics for Billu

Question

i) A box is divided into 9 equal sized compartments. A ball thrown in the box is equally likely to go into any one of these compartments. If 9 balls are thrown, calculate the probability for a particular compartments to contain (i) one particular ball only (ii) all the nine balls (iii) one of the balls.

Answer 1

(i)One particular ball

Let all balls be named from 1 to 9. Now for any particular ball, say ball "3", we want to find the probability of it falling into the considered compartment. Since the balls are equally likely to fall into any of the compartments, the probability of any particular ball falling in a particular compartment is 1/9.

The obtained probability is a result of the formula:

p = (favorable outcomes/total outcomes)

(ii)All the nine balls

Assuming each of the balls falling to be independent of each other, the probability of all nine balls falling into the same compartment will simply be equal to the product of each probability of the ball falling in that compartment.

$P(all\space nine \space balls)=p^9=\bigg(\dfrac{1}{9}\bigg)^9=2.5811748×10^{−9}$