Question

There are three caskets of treasure. The first casket contains 3 gold coins, the second casket contains 2 gold coins and 2 bronze coins, and the third casket contains 2 gold coins and 1 silver coin. You choose one casket at random and draw a coin from it. The probability that the coin you drew is gold has the value a/b, where a and b are coprime positive integers. What is the value of a+b?

Answer 1

you pick at a casket at random, so the probability you pick one any specific casket is \(\frac{1}{3}\) multiply and add
\[\frac{1}{3}\times 1+\frac{1}{3}\times \frac{2}{4}+\frac{1}{3}\times \frac{2}{3}\]

Answer 2

second number being the probability you pick a gold coin from the first, second or third casket respectively

Answer 3

compute this number,then add the numerator to the denominator
why that is part of the question is typical math teacher nonsense to put another level of annoyance in the problem