Help with this probability question?

The question:

To test a new program, the computer selects a random real number A from the interval [1, 2] and has the program solve the equation 3 x + A = 0. Find the probability that the root of this equation is less than –0.4.

Answer = 0.8

I'm not sure why the answer is this,

My working involved solving 3x+A =0 for x when A = 1 and 2 and I got x = -1/3 and -2/3. I know out of the 2 values -2/3 < -0.4 so I thought the answer would be 1/2 so I'm not sure

Reply 1

Can'tDecideAName

We know x = -A/3, a can be any real number from 1 to 2.

If x < -0.4 then A/3 > 0.4
so A > 1.2
as you can see, if A > 1.2 then 80% of all real values between 1 and 2 can be used as it is the interval (1.2,2] rather than [1,2]

Reply 2

Can'tDecideAName

I didn't express my reasoning greatly but chalk it up to me writing this at 3am :smile:

Reply 3

MonoAno555

Original post by Can'tDecideAName

I didn't express my reasoning greatly but chalk it up to me writing this at 3am :smile:

Thanks. Definitely understand the algebra now. The concept of 80% of real numbers can be written as 2-1.2/2-1 = 0.8 for the ratios of 1.2:2 and 1:2 for which A>1.2