Let f(x) = 1 if x is rational and 0 if x is irrational. If x is chosen at random between 0 and 1 what is that probablity f(x)=1?
2006-11-13 10:37:59 · 8 answers · asked by clamcrunchies2 2 in Science & Mathematics ➔ Mathematics
The rationals are a countable subset of [0,1], which
is an uncountable set. The probability that f(x) = 1
is therefore 0.
2006-11-13 11:12:10 · answer #1 · answered by steiner1745 7 · 1⤊ 0⤋
There are infinitely more irrationals than rationals in any interval, therefore the probability of a randomly chosen x being rational is infinitesimally small.
A method of choosing x is not obvious. But, for example, we could randomly choose integers a >= 2 and b >= 1, and say that we are using them to randomly choose x = 1/(a^(1/b)). Then we do have x between 0 and 1, but it is rational for b = 1 and irrational in almost every other case. I am sure there is some similar function which would give x uniformly distributed from 0 to 1 and still the same overwhelming proportion of irrationals.
2006-11-14 06:29:54 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Since 0 and 1 are both rational, and no irrational numbers lie between them, then 100% probability that f(x) = 1.
2006-11-13 10:41:35 · answer #3 · answered by maddojo 6 · 0⤊ 2⤋
I would say 50% because there is both an infinite number of rational and an infinite number of irrational numbers between 0 and 1.
2006-11-13 10:40:46 · answer #4 · answered by polloloco.rb67 4 · 0⤊ 1⤋
in case you advise 5x^2-50x+a hundred twenty five=0-------each and each variety has 5 as ingredient 5(x^2-10x+25) -----------start to ingredient, do not forget the 5 5 (x-5) (x-5) -----------the variety in the middle is made by ability of addition and subtraction in basic terms, the variety on the tip is made by ability of multiplication in basic terms (x-5)=0 (x-5)=0----set the two certainly one of them equat to 0 x= (-5, -5) The Martian is a million/2 maximum suitable after all. verify the respond with variety 5, and it will artwork. however the variety -5 will additionally artwork besides. yet sorry, i don't comprehend what number arms do an regularly occurring Martian has in any respect. A: x= (5, -5).
2016-10-22 01:02:09 · answer #5 · answered by lorentz 4 · 0⤊ 0⤋
probablity is 1. Because any random number chosen (by computer) will be finite in length and hence rational.
2006-11-13 13:21:36 · answer #6 · answered by Sora Aoi 2 · 0⤊ 1⤋
1 of course
2006-11-13 10:48:53 · answer #7 · answered by kkmalts 2 · 0⤊ 1⤋
50%
2006-11-13 10:53:40 · answer #8 · answered by Anonymous · 0⤊ 1⤋