Question

Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 30 to 70. What is the probability that this experiment results in an outcome less than 40?

Answer 1

A uniform random variable comes from a uniform distribution. In such a distribution, each event has the same probability of occurring. In this case, you have 40 events; that is, each score between 30 and 70 inclusive.

The probability of obtaining any one of these scores is then \[P=\frac{1}{40}\]Since each of these events is mutually exclusive (one person can't get two or more scores, only one), the probability of obtaining a score less than 40 is\[P(X<40)=P(X=\frac{1}{30} \cup \frac{1}{31} \cup...\cup \frac{1}{39})\]=\[P(\frac{1}{30})+P(\frac{1}{31})+...+P(\frac{1}{39})=\frac{1}{40}+\frac{1}{40}+...+\frac{1}{40}\]\[=\frac{9}{40}\]

Answer 2

Note, I assumed you wanted the probability of obtaining a score STRICTLY less than 40.

Also, \[P(X<40)=\frac{10}{40}=\frac{1}{4}=25%\]not the 9/40 I wrote above (you have 10 data points for X<40, not 9 - my bad).

Answer 3

And for scores between 30 and 70 inclusive, you have a total of 41 possible events, not 40...made the same mistake.

So\[P(X<40)=\frac{10}{41}\]