## amonaroll32 2 years ago Help?

1. amonaroll32

A real number x is chosen at random such that -2<=x<=5. What is the probability that x^2<2?

2. hwtrain

Do you mean?\[-2\le x \le5\]

3. amonaroll32

Yeah @hwtrain

4. zimmah

Assuming each of the values has equal probability of occurring, you can have any value including and between -2 and 5 equally likely. Which of these numbers when squared will result in a value smaller than 2?

5. zimmah

Since it's a suffienctly small sample you can just try them each if you are not sure if they are smaller than 2 when squared

6. amonaroll32

@zimmah There is an infinite number (decimals count)

7. zimmah

8. zimmah

Then, a slightly different approach is needed

9. zimmah

Since the number squared has to be smaller than 2, the number itself must be smaller than the root of two, but since it's squared also negative numbers will result in positive so every value between -sqrt2 and +sqrt2 would do

10. amonaroll32

So would it be 2(sqrt2) over 7?

11. zimmah

Then, you should probably get the ratio of -sqrt2 to -2 to see how much chance you have forthwith neat tsing of the line, and the same for the positive side.

12. zimmah

I guess so. I'm not 100% certain but sounds about riht

13. amonaroll32

Thanks!

14. zimmah

Sorry for my spelling but theis website has horror input lag on ipad and also autocorrect from ipad tesla :s