Conditional Probability for a Uniform Distribution

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.

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