Question

. Chest A has 100 gold coins, and chest B has 50 gold and 50 silver coins. You randomly choose a treasure chest to open, and then randomly choose a coin from that treasure chest. If the coin you choose is gold, then what is the probability that you chose chest A? (Use Bayes theorem)

Answer 1

Chest A has 100 gold coins an chest B has 5 gold and 50 silver coins.

Here probability to select any chest = 1/2

Now we will randomly chose a coin and that is gold.

Here

Probability that we chose chest A if selected coin is gold.

P(Selected coin is gold) = P(selected first chest) * P(Got a gold coin) + P(Selected second chest) * P(Selected a gold coin)

= 1/2 * 1 + 1/2 * 1/2 = 3/4

Now by bayes theorem

P(Selected chest is A if selected coin is gold) = P(selected coin is gold if selected coin is from chest A) * P(Selected coin is gold one)/ P(Selected coin is gold)

= (1/2 * 1)/(3/4) = 2/3