ODDS game. Odds of me and my friend picking same number 1-100

We play a game where you say 'what are the odds of you doing a certain event'

Eg 'what are the odds of you going out in a vest tonight'

'1 in 100'

'Okay'

'3,2,1 (both say number between 1 and 100)

What are the odds of us both saying the same number?

I say it's a 1 in 100 chance

My friend thinks it's a 1 in 10,000 chance

Please clarify!

Thank you

Reply 1

rayquaza17

17

The probability of choosing the same number is 1/100.

The odds of choosing the same number are 1:99.

There's a difference between probability and odds.

But there are 10,000 possible outcomes of possible pairs of numbers you could both pick (1,1), (1,2), (1,3), ... etc but only 100 possible outcomes where these match (1,1), (2,2), ..., (100,100) so you work out the probability of picking the same number by:

number of outcomes where they match / total number of outcomes = 100/10000 = 1/100.

Your friend has thought: I have 1/100 chance of choosing a particular number, and you have 1/100 chance of choosing a particular number so the probability they are the same is (1/100)*(1/100)=1/10000. This is incorrect because you asked us "the probability they are the same number", not "the probability we both pick a certain number".

To understand where the 10,000 possible outcomes, consider a simpler example: Choosing a number between 1 and 3.
The outcomes are (1,2), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) there are 9 outcomes. 9=3*3. In your case there are 100 choices for each, and 100*100=10000.

So just to expand on the TenofThem's answer below, the probability of you both picking a particular number is 1/100 * 1/100 = 1/10000 but the probability you pick the same number is 1/100 because there are 100 ways you can both pick the same number, but only 1 way you can both pick any particular number.

Hope this makes sense. Probability isn't my strong point, and I think questions like this can really confuse people!

(edited 9 years ago)

Reply 2

TenOfThem

18

Original post by GemmaSmith

We play a game where you say 'what are the odds of you doing a certain event'

Eg 'what are the odds of you going out in a vest tonight'

'1 in 100'

'Okay'

'3,2,1 (both say number between 1 and 100)

What are the odds of us both saying the same number?

I say it's a 1 in 100 chance

My friend thinks it's a 1 in 10,000 chance

Please clarify!

Thank you

Ignoring the fact that you confuse "odds", "chance". and "probability"

The probability that you both choose 45 (for example) is

\dfrac{1}{10000}

The probability that you choose the same number is

\dfrac{100}{10000} = \dfrac{1}{100}

(edited 9 years ago)

Reply 3

BabyMaths

Original post by TenOfThem

Ignoring the fact that you confuse "odds", "chance". and "probability"

The probability that you both choose 45 (for example) is]tex]\dfrac{1}{10000}

The probability that you choose the same number is

\dfrac{100}{10000} = \dfrac{1}{100}

Do people generate random numbers? :biggrin:

Reply 4

rishich101

1

You are correct because you have 100 numbers to pick from and your friend also has 100 numbers to pick from. so the possible combinations are 10000 and you both can get the same numbers with 100 different numbers. So the probability is 100 in 10000 which is 1 in 100 chance. Your friend probably was thinking about 10000 different pairs.

ODDS game. Odds of me and my friend picking same number 1-100

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