# Probability puzzle debate

#### MikeT

##### New Member
During the current lockdown, our quiz group has been entertaining ourselves with various puzzles. A probability from Le Monde newspaper has engendered considerable debate amongst our little group. Since none of us are statisticians I'd like to ask the forum for their opinion on the two contested answers.

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?

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

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 ?

#### obh

##### Well-Known Member
Hi Mike,

Try the conditional probability formula:

P(A|B)=P(A∩B)/p(B)

A -leather bag
B - gold coin

Please show me, step by step how you solve.
1. What is P(leather bag ∩ gold coin)?
2. What is P(gold coin)?
3. P(leather bag | gold coin)?

#### MikeT

##### New Member
P(A&B) = 20/90
P(B) = 40/90
P(A|B) = 50% ....... which (I think) uses the same methodology as answer two.

#### obh

##### Well-Known Member
A ∩ B is the probability for gold coin in the leather bag...

#### MikeT

##### New Member
Which is 20 gold coins out of 90 coins total (as above) - or should it be 20 gold coins out of 40 coins in the leather bag?