Maths: Probability Distribution

Question

Suppose X is a uniform random variable between 0.50 and 1.00.

What is the probability that a randomly selected value of X is between 0.55 and 0.60 or between 0.75 and 0.85?

A. 0.00

B. 0.15

C. 0.60

D. 0.30

Answer 1

Uniform random variable X with parameter a,b:

F(X)=$\frac{1}{b-a}$

F(X)=2 ,a=.5 and b= 1.

To find probability distribution of the interval (0.55,0.60) and (0.75 , 0.85), find the area of the region they cover.

Probability (X)= area 1 + area 2

area 1 :- As it will make rectangle with height=2 and width=0.60-0.55=0.05. Area1= 0.05*2=0.1

area 2 :- 

As it will make rectangle with height=2 and width=0.85-0.75=0.1. Area1= 0.1*2=0.2

Probability = 0.1+0.2=0.3

https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)

Answer 2

1.00-0.50= 0.50 (Total case)

0.60 to 0.55 = 0.05, 0.85-0.75=0.10

0.05+0.10=0.15 (favorable case)

Probability = $\frac{0.15}{0.50}$=0.3

Comments

probability= (6c1 + 11c1 )/ 51c1 = .3333
isn't this correct solution??

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How did you get 6c1 and 11c1