Question

HELP! I ONLY HAVE 5 MINS LEFT! You and 15 other people are at a party. The host tells you that they have placed one special item in a bag with 16 items total. The host says that there is an 80% chance that the special item is still in the bag, and a 20% chance that it was taken out.

The host passes the bag around and each person selects an item at random. You decide to keep your item hidden while everyone else shows theirs, and no one finds the special item. What are the odds that the special item is in your item?

Answer 1

67.5%

Explanation:

There is a 67.5% chance that the special item is in your bag.

The initial probability that the special item is in the bag is 80%.

The probability that the special item is not in the bag is 20%.

The probability that the special item is not in any of the other 15 bags is 15/16 * 14/15 * 13/14 * ... * 3/4 * 2/3 = 1/2.

The probability that the special item is in at least one of the other 15 bags is 1 - 1/2 = 1/2.

The probability that the special item is in your bag is 80% * 1/2 = 67.5%.

Here is a breakdown of the probabilities:

* The special item is in the bag: 80%

* The special item is not in the bag: 20%

* The special item is in one of the other 15 bags: 1/2

* The special item is in your bag: 67.5%