Question

A coder programmed a random number generator, which generates a random number between 0 and 1 when the user presses the "random" button. Numbers generated follow a uniform distribution.

12- What is the probability the next time the button is pressed the code will generate a number less than .23?

13- What is the probability the next time the button is pressed the code will generate a number between .23 and .35?

14- What is the probability the next time the button is pressed the code will generate a number between .23 and .35 or between .45 and .50?

15- What is the probability the next time the button is pressed the code will not generate a number between .23 and .35 or between .45 and .50?

Answer 1

Given that, X ~ Uniform ( a = 0, b = 1)

We want to find, the following probabilities,

Q.12) P(X < 0.23) = ( 0.23 - 0) / (1 - 0) = 0.23

Therefore, the probability the next time the button is pressed the code will generate a number less than .23 is 0.23

Q.13) P(0.23 < X < 0.35) = ( 0.35 - 0.23) / ( 1 - 0) = 0.12

Therefore, the probability the next time the button is pressed the code will generate a number between 0.23 and 0.25 is 0.02

Q.14) P(0.23 < X < 0.35) = 0.12

P(0.45 < X < 0.50) = 0.05

P(0.23 < X < 0.25) OR P(0.45 < X < 0.50) = 0.02 + 0.05 = 0.07

Therefore, the probability the next time the button is pressed the code will generate a number between .23 and .35 or between .45 and .50 is 0.17

Q.15) 1 - 0.17 = 0.83

Therefore, the probability the next time the button is pressed the code will not generate a number between .23 and .35 or between .45 and .50 is 0.83