What does less than mean in the sentence "How many characteristics need to be considered so probability of 2 people having this number of characteristics is less than 1/3000000000"
What does less than mean?
- Posted:
- 3+ months ago by PleaseHel...
- Topics:
- people, number, numbers, sentence, probability
Details:
Responses (1)
Well, that depends on how many people have this or that characteristic. Let's think about tossing coins. If one person tosses a coin it can land two ways: heads or tails. So the odds are 50%. If two people toss coins, there are four ways they can land, and two of them are the same (both heads or both tails), so the odds are 50%. If three people toss coins there are eight ways they can land, and still only two are the same so the odds have now decreased to two out of eight or 25%. If N people toss coins there are 2^N ways they can land, and always two are the same, so the odds are 2/2^N or 1/2^(N-1).
Now assuming you are talking about tossing coins, you want to find a value of N where 1/2^(N - 1) < 1/3000000000 which we can write 2^(N - 1) < 3 x 10^9
But you don't say what you are talking about, so you have to do the analysis yourself.
I made a mistake there. 2^(N - 1) < 3 x 10^9 should be 2^(N - 1) > 3 x 10^9. That is, a larger number under the fraction bar makes the fraction smaller.
As I said, this only applies to tossing coins. If you have something else, you have to do the entire process with different numbers.
Alright sir, thank you for your assistance.
Would 2^(N - 1) < 3 x 10^9 be the final answer assuming we were talking about tossing coins?