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- [Instructor] In the previous movie,
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I described how to calculate simple probabilities,
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that is the probability of a single trial.
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In this movie, I will describe compound probabilities.
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Compound probabilities assume that you
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want to analyze multiple independent trials.
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And by independent, that means that the second trial
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or outcome, in other words, the second flip of a coin
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or a throw of a die, is independent of the first.
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If you do have multiple independent trials,
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then you will multiply probability
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to get a compound probability.
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So flipping a coin will end up on heads half the time.
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So the probability of getting heads twice in a row
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assuming that the coin is fair
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would be one half times one half equals one quarter.
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One easy mistake to make is
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to assume that compound probability
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after you've already started.
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In other words, one of the trials has been done.
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If you're flipping a coin,
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again, a fair coin,
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with a one half probability of getting heads
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and you flip and get heads,
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the probability of flipping heads twice in a row
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is no longer one quarter.
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It is one half because you've already done it once.
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And all that matters is the second trial
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which is 50% or one half likely to end up on heads.
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To visualize the probabilities,
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I have created a chart.
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And you can see that I have two separate trials in the rows.
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In the first we have independent outcomes rolling a die.
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And we're asking the probability
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of rolling a three on the first outcome
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and rolling a three again on the second one.
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Assuming everything is independent,
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then we have one chance out of six,
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each of those trials to come up a three.
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So that would be 1/6 times 1/6 equals 1/36.
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So we have one chance out of 36
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or 35 to one odds against.
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We might also ask what is the probability
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of rolling exactly a three on the first outcome
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and not rolling a three,
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in other words getting any other number
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on the second outcome?
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Well, for that, we have our probability of 1/6
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of rolling a three,
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and then we have five out of six numbers
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that would allow us to succeed in our scenario.
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So we multiply 1/6 by 5/6,
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and get 5/36.
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And those numbers make sense.
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If we look back at the first row
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and we see that we have 1/36 of rolling a three,
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if we add that to 5/36 in the second row
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where we don't roll a three,
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we get 6/36, which is 1/6,
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and is the probability of rolling a three
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in the first place.
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Compound probabilities can get a little tricky,
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but after you make sure
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that the results of your trials are independent
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you can use multiplication to find
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the compound probability of the composite outcome
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you're looking for.
5127
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