The Question

On a desert island, a pirate has buried two bags of treasure a few metres apart:

a jute bag containing 20 gold coins and 30 silver coins

a leather bag containing 20 gold coins and 20 silver coins

Unfortunately for him, he dies in prison without returning for his treasure.

Many years later, an explorer lands on the island and starts digging. As luck would have it, he finds one of the two bags. He puts his hand into it and brings out a coin at random.

If the coin is gold, what is the probability that he has found the leather bag?

Answer One

Probability of drawing gold from leather bag is 20/40 =0.5

Probability of drawing gold from jute bag is 20/50=0.4

Probability of gold coin drawn from leather bag = 0.5/(0.5+0.4) = 5/9

Answer Two

Once gold coin has be been drawn, we know that it is gold so the silver coins are irrelevant to the calculation.

So 20 gold coins in leather bag and 20 gold coins in jute bag, therefore probability of leather bag is 20/(20+20) = 50%

Which of the answers are correct ?