If I have 5 items and 2 people pick one each at random, what is the probability they will pick the same one?

Question

If I have 5 items and 2 people pick one each at random, what is the probability they will pick the same one?

Answer 1

Interesting split of opinions here. The answer is 1 in 5 (or 1/5, or 20%)

Assuming that once an object at random, the object is still available to the other person.

To convince you that 1/5 is right and 1/25 is wrong, I will write out each possibility. The people are called A and B, and the items are numbered 1 to 5. So A:2 B:3 means person A picked item 2 and person B picked item 3.

Here are all the possibilities, and the ones with the * next to them are the ones where both peopled picked the same item.

Notice that there are 25 combinations, but only 5 of them match our requirement. So the probability is 5/25 = 1/5.

A:1 B:1 *

A:1 B:2

A:1 B:3

A:1 B:4

A:1 B:5

A:2 B:1

A:2 B:2 *

A:2 B:3

A:2 B:4

A:2 B:5

A:3 B:1

A:3 B:2

A:3 B:3 *

A:3 B:4

A:3 B:5

A:4 B:1

A:4 B:2

A:4 B:3

A:4 B:4 *

A:4 B:5

A:5 B:1

A:5 B:2

A:5 B:3

A:5 B:4

A:5 B:5 *

Answer 2

My thinking is 1 out of 5 chance as there are only 5 objects and only 1 can be selected. But don't know if that is right looking at the other answers.

Don't understand how they could have a 1 out of 25 chance when there are only 5 items??

Answer 3

If they aren't replaced, 0%

if they are replaced, 1/5

Answer 4

Well the balance of opinion is in favour of Nick J, which is correct.  Someone has also gone into great lengths to itemise each possibility..so well done to him/her too !

Answer 5

Most likely is 1/5 as there are five items.

Answer 6

How can Same thing picked up by 2 different persons? when one picks it, it s not there for the second to 'pick' it up.

Under the given conditions I think it is 0.

If they are writing their preferences [like in window shopping] then yes it is (1/5)^2 = 1/25

Answer 7

The correct answer is 1/5, or 20%, as several have pointed out, and correctly explained.  

The # of people who picked 1/25 explains why so many people play the lottery - they don't know how to figure the odds of winning, and see how slim their chances really are.

Answer 8

"mathmaniac" is right. It doesn't matter what the first person picks. Once s/he has made her/his choice, then there is a 1/5 or 20% chance that the second person will choose the same one.

QED

Answer 9

(1/5)*(1/5)=(1/25)

In other words, 1 out of 25 chance.

Answer 10

No, I was wrong. it's 1/5

Answer 11

There are altogether 5*5=25 possibilities, but only 5 of these satisfies what you want, hence 5/25=1/5

Answer 12

1 in 5

The first one picks any item - it does not matter which one - then the chance that the second person will pick the same one is 1 in 5.