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We are told that 21 % of this population suffer from depressive -like symptoms.
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We are taking a sample of eight people in this age group.
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Probability each experiences depressive -like symptoms will be 21%.
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0 .21.
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This is going to follow a binomial distribution.
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N independent trials, each member of the random sample.
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Two outcomes for each they experience this or they do not.
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Same probability p that each does.
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Now, in part a, we want to...
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The probability none of them experience these symptoms.
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Probability x number in the sample that meets this criteria is equal to 0.
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This is the same thing happening eight times in a row.
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Because these are independent of each other, we can combine their probabilities by multiplying.
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So it's a probability of the first person does not have such symptoms, 79%, multiplied by the probability the second doesn't, 79%, and so on and so on, eight times in a row.
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Notice i'm using decimal form, percentages do not play well with calculations.
01:04
And this is no point, 15, 17 to four decimal places.
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Part b, probability at least two meet the criteria.
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Now i'm going to use the binomial formula.
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Probability exactly x is n choose x, p to the x, 1 minus p to the n minus x.
01:24
For part a, this would be very simple.
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This is the number of orders we can put them in.
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There's only one way to put eight of the same thing.
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In order, so that was 1...