probability question

Question

given three identical boxes I,II,III each containing 2 coin.in box I,both coins are gold,in bow II both are silver, in box III ,there is 1 gold and one silver.A person chooses a box at random and takes out a coin.if the coin is gold,what is the probability that the other coin is also of gold?

Answer 1

This is best approached by making a probability tree diagram,I believe.

 

Prob of choosing each box is 1/3.

In case of choosing #I, both choices will be gold.

In case of choosing #II, neither will be gold.

In case of choosing #III, P(gold on first try is 1/6, because it's product of 1/3 (choice of box) times 1/2, prob. of gold within this choice.

 

This is a conditional probability problem: P(gold on 2nd|gold on first) = P(gold∩gold) / P(gold on 1st)

= (1/3) / [1/3 + 1/6] = 2/3.