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Ex: Determine the Probability of a Union Using a Table - Not Mutually Exclusive - YouTube
Channel: Mathispower4u
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the table summarizes results from 976
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pedestrian deaths that were caused by
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automobile accidents notice how the
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table indicates whether the pedestrian
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was intoxicated
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as well as whether the driver was
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intoxicated if one of the pedestrian
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deaths is randomly selected find the
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probability that the pedestrian was not
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intoxicated or
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the driver was intoxicated
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so in this case we're trying to
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determine the probability
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of a union of two events
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and because these two events can occur
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at the same time
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the two events are not mutually
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exclusive and therefore we'll apply the
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probability formula given here below
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where if it is possible for two events
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to occur at the same time
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the events are not mutually exclusive
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and therefore the probability of a or b
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equals the probability of a plus the
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probability of b
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minus the probability of a and b
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and we'll see in this problem why
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we have to subtract this probability
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here
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so to set this up
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we'll say the probability the pedestrian
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was not intoxicated
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or the driver was intoxicated
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is equal to the probability the
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pedestrian was not intoxicated plus
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the probability that the driver was
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intoxicated
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and then minus the probability the
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pedestrian was not intoxicated and the
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driver was intoxicated
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now we'll determine each of these
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probabilities so to begin
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we'll determine the probability
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the pedestrian was not intoxicated
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and notice how we can determine that
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information from this column here
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this column indicates
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the number of pedestrians that were not
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intoxicated
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and since 82 plus 606 is equal to 688
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the probability that the pedestrian was
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not intoxicated
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would be 688
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divided by
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the total number of deaths which is 976
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and then we have plus
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the probability that the driver was
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intoxicated
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and notice how this row here indicates
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the number of drivers that were
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intoxicated
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and therefore the probability that the
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driver was intoxicated would be equal to
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62 plus 82 which is 144
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divided by
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976
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but notice how in these two
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probabilities we counted these 82 depths
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twice
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and these 82 deaths were when the
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pedestrian
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was not intoxicated and
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when the driver was intoxicated and this
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is the reason why
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we have to subtract this last
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probability
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which again is the probability
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that the pedestrian was not intoxicated
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and the driver was intoxicated which
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would be 82
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divided by
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976.
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now let's go and express this
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probability
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as a simplified fraction decimal and
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percent
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so let's go to the calculator
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notice how we already have a common
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denominator
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so the numerator is going to be
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in parentheses 688
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plus 144
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minus 82
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and all this is divided by
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976
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so we'll press enter
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this gives us a decimal approximation
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but if we press math enter enter
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this gives us a simplified fraction
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which is 375
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over 488
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so this would be the exact probability
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but the directions do ask us to enter a
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percentage rounded to one decimal place
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so we'll first convert this to a decimal
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and because we want the percent to be to
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one decimal place
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we'll have to round the decimal to three
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decimal places
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so going back to the calculator notice
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how this would be approximately 0.768
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so approximately 0.768
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converting to a percentage we multiply
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by 100 and add a percent sign
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or move the decimal point to the right
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two places giving us approximately
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76.8 percent
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i hope you found this helpful
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