There are two boxes, each containing one marble. A marble is either red or green
ID: 2921907 • Letter: T
Question
There are two boxes, each containing one marble. A marble is either red or
green, with probability 50% each.
(a) What is the probability that both marbles are green?
(b) Someone randomly chooses one of the boxes and opens it. What is the probability that
both marbles are green if the revealed marble is green?
(c) Instead of choosing randomly, the person rst peeks into both boxes, then opens one
using the policy, that if any of the boxes contains a green one, then he always chooses
to reveal a green marble. What is the probability that both marbles are green if the
revealed marble is green?
Explanation / Answer
a) Probability that both marbles is green is computed as:
= Probability that first marble is green * Probability that the second marble is green
= 0.5*0.5
= 0.25
Therefore 0.25 is the required probability here.
b) Given that one of the marble is green probability that both the marbles would be green is computed using Bayes theorem as:
= Probability that both are green / Probability that one of them is green
= 0.25 / 0.5
= 0.5
Therefore 0.5 is the required probability here.
c) Here even when both the marbles are green, then one of the box opened would be the green one. And if one is red, one is green then the green one will be showed.
Now as a green marble is shown this means that the prior colours of the 2 marbles would be any one of GR, RG or GG. Therefore, probability that both are green is computed as:
= Probability of GG / Probability of { RG, GR, GG }
= 1/ 3
= 0.3333
Therefore 0.3333 is the required probability here.