SOLUTION: let x be a uniform random over the interval (0.1,5) what is the probability that the random variable x has a value less than 2.1

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Question 1201065: let x be a uniform random over the interval (0.1,5) what is the probability that the random variable x has a value less than 2.1
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

This probability is the ratio of the lengths of two intervals.


The shorter interval is  2.1-0.1 = 2 units long.


The longer interval is 5-0.1 = 4.9 units long.


The probability under the problem's question is   = 0.4082 (rounded).      ANSWER

Solved.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Refer to this diagram

The red segment (A) spans from 0.1 to 2.1
Its length is 2.1-0.1 = 2 units

The blue segment (B) goes from 0.1 to 5
length of B = 5-0.1 = 4.9

The chances of landing in region A is
A/B = 2/4.9
A/B = 0.40816326530612
A/B = 0.40816
This approximately is about a 40.816% chance of happening.
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