# Conditional Probability for a Uniform Distribution

0:00:00.000,0:00:06.066 This is a video on conditional probability

and the uniform distribution. 0:00:06.066,0:00:14.000 The question states: The minutes after the

hour when a baby is born is uniformly 0:00:14.000,0:00:22.066 distributed from 0 to 60. Find the probability that the minutes after the hour that a baby will 0:00:22.066,0:00:31.066 be born is less than 40 given that it is greater than 10. Let’s start by drawing a picture 0:00:31.066,0:00:38.000 that will help make sense of this question. We know that the largest the number of minutes 0:00:38.000,0:00:45.066 can be is 60. We are also told that we are given that it is greater than 10. That means 0:00:45.066,0:00:53.066 we’re not going from 0 to 60, rather we’re

going from 10 to 60. That length between 10 and 0:00:53.066,0:01:01.066 60 is 60 minus 10 which is 50. For the area of the full rectangle to be equal to 1, 0:01:01.066,0:01:14.033 the height must be 1/50, because 1/50 times

50 is 1. We want to find the probability that the 0:01:14.033,0:01:21.066 minutes after the hour will be less than 40. We want to find the area of the subrectangle 0:01:21.066,0:01:31.066 to the left of 40. The area of a rectangle is the base times the height. We can say the 0:01:31.066,0:01:38.066 probability that x is less than 40 given that

x is greater than 10 is equal to the base 0:01:38.066,0:01:46.000 and the base length is 40 minus 10. That length is 30, times the height. The height of the 0:01:46.000,0:01:59.033 rectangle is 1/50. Now I just calculate. 40 – 10=30. 30/50 reduces to 3/5. 0:01:59.033,0:02:08.033 Now I am ready to state my conclusion. I can conclude the probability that the minutes 0:02:08.033,0:02:15.000 after the hour that a baby will be born is

less than 40 given that it is greater than 10 0:02:15.000 is 3/5. I am done with the problem.

## 3 Replies to “Conditional Probability for a Uniform Distribution”

That was helpful

Much simpler than the method my prof. "taught" us. Very helpful thanks for the upload.

Enter an exact number as an integer, fraction, or decimal.

P(15 < x | x < 26) = Help me fam