A small problem to peruse.

Jenn said:

Any non 50% guesses should be accompanied by a bit of reasoning please :)
 
imightbewrong said:
Any non 50% guesses should be accompanied by a bit of reasoning please :)
Well if he picks an apple first it means he's picked from either the all apple basket or the apple and orange basket.
If he picked the apple from the all apple basket, there's 100% (or 1 out of 1) chance that the second pick is an apple.
If he picked the apple from the apple and orange basket there's 50% (or 1 out of 2) chance that the second pick is an apple.

So in total there's 2 chances out of 3 that the second pick will be an apple (or 66%).
 
Jenn said:
Well if he picks an apple first it means he's picked from either the all apple basket or the apple and orange basket.
If he picked the apple from the all apple basket, there's 100% (or 1 out of 1) chance that the second pick is an apple.
If he picked the apple from the apple and orange basket there's 50% (or 1 out of 2) chance that the second pick is an apple.

So in total there's 2 chances out of 3 that the second pick will be an apple (or 66%).

Bravo. Basically when he shows you an apple one of three equally likely things has happened

- He went to the Apples basket and is showing you his left hand
- He went to the Apples basket and is showing you his right hand
- He went to the Apples & Oranges basket

The first two lead to an apple in his other hand, hence a 2/3s chance of second apple.

I like to ask this one to inteview candidates and watch their face make funny shapes while they figure it out.
 
imightbewrong said:
Bravo. Basically when he shows you an apple one of three equally likely things has happened

- He went to the Apples basket and is showing you his left hand
- He went to the Apples basket and is showing you his right hand
- He went to the Apples & Oranges basket

The first two lead to an apple in his other hand, hence a 2/3s chance of second apple.

I like to ask this one to inteview candidates and watch their face make funny shapes while they figure it out.

I had to put it to paper to be honest. :)
And I wasn't that good at statistics at school but I obviously picked up the basics.

To be honest I don't think these tests give an accurate indication on a person's ability to do their job (unless they're applying to work with statistics !). I can't remember the last time I had to use statistics in my job.
And as for the first test posted here, in real terms you'd open all the baskets, swear a bit then phone your supplier and have a go at them ;) ; not spend time working out the result by taking a fruit here and there.
 
Any chance of some more?
 
That can't be right.If he chose an apple from the mixed box then it's 100% that the other 'hand' is an orange as you stated he took 1 of each fruit from that box!

ie pick from orange box-neither can be apples
pick from apple box,both will be apples so 100% chance other 'hand ' is an apple
pick from mixed box,one of each fruit,if first is apple other must be orange so 0% chance

I still make it 50%
 
Jenn said:
I had to put it to paper to be honest. :)
And I wasn't that good at statistics at school but I obviously picked up the basics.

To be honest I don't think these tests give an accurate indication on a person's ability to do their job (unless they're applying to work with statistics !). I can't remember the last time I had to use statistics in my job.
And as for the first test posted here, in real terms you'd open all the baskets, swear a bit then phone your supplier and have a go at them ;) ; not spend time working out the result by taking a fruit here and there.

Sure. The bulk of the interview is usually job-specific technical questions, but if they're going for a moderately senior developer role, I like to see how they approach logic problems since that's what they'll be doing a lot of the time. I don't mind them writing something down - or even getting it wrong - but seeing some sort of logical approach is important (I think).
 
imightbewrong said:
Sure. The bulk of the interview is usually job-specific technical questions, but if they're going for a moderately senior developer role, I like to see how they approach logic problems since that's what they'll be doing a lot of the time. I don't mind them writing something down - or even getting it wrong - but seeing some sort of logical approach is important (I think).

Am I hired then? ;)
 
Drd said:
That can't be right.If he chose an apple from the mixed box then it's 100% that the other 'hand' is an orange as you stated he took 1 of each fruit from that box!

ie pick from orange box-neither can be apples
pick from apple box,both will be apples so 100% chance other 'hand ' is an apple
pick from mixed box,one of each fruit,if first is apple other must be orange so 0% chance

I still make it 50%

This is what most people think - and is what seems logical at first glance. However what you need to factor in is that there are three possible states, not two as you have above.

1 - Apples basket - hand 1 (1/3 chance)
2 - Apples basket - hand 2 (1/3 chance)
3 - Mixed basket - apple hand (1/3 chance)

This problem is very similar to this classic:

You are on a game show with three doors. One contains a prize. You choose a door at random. The host then eliminates one of the other two doors, guaranteeing not to remove the prize door. He then asks if you want to change your mind to the other door, or stick with your initial choice.

Would you change your mind, and why?
 
imightbewrong said:
This is what most people think - and is what seems logical at first glance. However what you need to factor in is that there are three possible states, not two as you have above.

1 - Apples basket - hand 1 (1/3 chance)
2 - Apples basket - hand 2 (1/3 chance)
3 - Mixed basket - apple hand (1/3 chance)

This problem is very similar to this classic:

You are on a game show with three doors. One contains a prize. You choose a door at random. The host then eliminates one of the other two doors, guaranteeing not to remove the prize door. He then asks if you want to change your mind to the other door, or stick with your initial choice.

Would you change your mind, and why?


Think I know that one

*****Answer spoiler*******Highlight text to read
.

Yes beacuse at first you have a 33% chance of getting the prize but if you pick again that increases to 50%.
 
WibXL said:
Think I know that one

*****Answer spoiler*******Highlight text to read
.

Yes beacuse at first you have a 33% chance of getting the prize but if you pick again that increases to 50%.

Not quite - can you explain how you came up with the probabilities?
 
imightbewrong said:
Not quite - can you explain how you came up with the probabilities?

Doh. At first it's a 1 in 3 chance that you'll get the prize and then when one is removed the choice becomes 1 in 2 if you pick again. But as this is pretty much identical to your other question I'm guessing the answer is the same:)

EDIT: Just found a good explanation here and I understand it now
 
WibXL said:
Doh. At first it's a 1 in 3 chance that you'll get the prize and then when one is removed the choice becomes 1 in 2 if you pick again. But as this is pretty much identical to your other question I'm guessing the answer is the same:)

EDIT: Just found a good explanation here and I understand it now

Yes that's the same mistake as is usually made on the other problem as well :) The solution is:

Another way of looking at this question is you have the option of sticking with your first choice (1 in 3 chance) or changing to BOTH of the other doors (2 in 3 chance). Hence you should change your mind for a 2/3 chance of winning.
 

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