Question

Help?

Answer 1

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

Answer 2

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

Answer 3

Yeah @hwtrain

Answer 4

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?

Answer 5

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

Answer 6

@zimmah There is an infinite number (decimals count)

Answer 7

My bad.

Answer 8

Then, a slightly different approach is needed

Answer 9

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

Answer 10

So would it be 2(sqrt2) over 7?

Answer 11

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.

Answer 12

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

Answer 13

Thanks!

Answer 14

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