If I have a choice of 32 types of locks for 16 homes what is that chance of 2 homes having the same type?

Answer 1

Another formulation of this problem is to say. I pick 16 samples on a choice of 32. What is the chance that one sample gets picked twice.

The total number of draws is 32 to the power 16. The total number of draw where the pick are all different is 32*31*;;;*17. So the probability they are all different is the product P=(32/32)*(31/32)*...*(17/32), and the probability that 2 (at least) are the same is 1 minus that probability. P, which is very close to 1.

Answer 2

The probability that at least 2 of the 16 home has the same type of lock is 1 in 1024.
1 in 32 that one of the homes has one type and one in 32 that another home has the same.
Multiply to get 1 in 1024.

Probability that exactly 2 have the same lock is 1 in 32^16

Answer 3

Suppose there are only two homes:
in that case the chance of different locks is 31/32 (because 1 of the 32 locks is already in use)

With three homes the chance is:
(31/32) x (30/32)

=> With 16 homes the chance is
(31/32) x (30/32) x (29/32) x ....... x (17/32) = 0.0104 or 1.04%

Answer 4

Are you sure you haven't got this round the wrong way? If you have 32 different types of locks and only 16 homes then you have no chance of 2 homes having the same type.

Answer 5

Do you mean the chance of exactly 2 homes having the same type, or at least 2 homes (i.e. the locks are not unique across the 16 homes)?

Answer 6

1 in 32 because if house a house lock type 1 then it is 1 in 32 that house b has the same type of lock...the question states that there are 16 houses and 32 types of locks not 32 locks

Answer 7

I took combinatorics and stats in college....gianlino's answer is the only one that is correct so far. Another way of saying it is this:

To determine the probability of "at least" two being duplicates you can first determine the probability of *none* of them being duplicates and subtract that from one. So the total possible combinations would be 32 to the 16th power (represented as 32^16 here). And the total number of possibilities where there are *no* duplicates would be P(32,16). (P(32,16) reads as 32 permutations of 16). So the final probability would be whatever is left over from discounting the probability of no duplicates. Therefore we have Prob = 1 - (P(32/16) / (32^16)) which comes out to 0.98959....in other words there is a 98.959% chance of "at least" two being duplicates.....choosing "exactly" two is a different story.

Answer 8

We moved into a brand new house in a cul-de-sac some years ago. There were 24 houses on the site. One day a neighbour came home from the pub and accidentally went to the wrong house. His back door key wouldn't work so he stumbled round to the front and tried the lock. His key opened the front door to his neighbours shock who was sat down stairs expecting her husband to walk in. Anyway, he was shown out the way he had come in, after the initial settlement and apologies. The next day the 2 met up to discuss the problem. They soon realised they could open each others door, and their neighbours door, and theirs, and so on until it was obvious everyone has access to everyone elses house!!!.

Answer 9

32 types of locks have 32 different key patterns.

I am not sure if 32 types of locks have the same brand name. Your statement daes not mention brand names.

I am not sure if 32 types of locks have the same physical specifications. your statement does not mention the specifications.

I am not sure if 32 types of locks have the same color. your statement does not mention color.

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Answer 10

if theres 32 different locks, and 16 different homes, very lock will be different...