Suppose that the wait time in the local coffe shop ranges evenly between 0 and 300 seconds.

a.) what is the probability that you will wait less than 100 seconds to be served?

b.) What is the probability that you will wait more than two minutes to be served?

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An "answer" someone gave me:

The wait time is a uniform random variable X between 0 and 300s. The probability density function is

f(x) = 1 / (300-0) = 1/300

Probability that wait time is less than 100s is

P(X<100s) = (x:0 to 100) ∫f(x)dx = (x:0 to 100) ∫(1/300)dx = [x/300](x:0 to 100) = 100/300 - 0/300 = 1/3

Probability that wait time is more than 2min (= 120s) is

P(X>120s) = (x:120 to) ∫f(x)dx = (x:120 to 300) ∫(1/300)dx = [x/300]{x:120 to 300} = 300/300 - 120/300 = 180/300 = 0.6

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I don't just want to "Write down" the "answers". Can someone please explain/show me what is going on here?

"p(x<100)" I understand, where the probability of x is less than 100. I don't understand what is happening after that, in both situations. What is a density function? I'm confused.