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Answer to Question #6182 in Statistics and Probability for Marilyn Davis

Question #6182
70% of married couples paid for their honeymoon themselves. You randomly select 20 married couples and ask each if they paid for their honeymoon themselves. Find the probability thaqt the number of cuples who say they paid for their honeymoon themselves is a)exactly one b) more than one, and c) at most one.
Expert's answer
a)exactly one
Let x- random variable, which represents amount of couples who paid for their honeymoon themselves.
Probability that couple paid for themselves= 0.7
That they doesn’t 0.3
We can use Bernulli’s formula here . Let’s recall it:
data:image/png;base64,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
where n-number of trials
k-number of successes
n-k – number of failures
p-probability of success in one trial
(1-p) – probability of failure in one trial

We have n=20 trials and each of them has two possible outcomes (paid themselves or not paid themselves) with probabilities p=0.7 and q=1-p=0.3
So we have due to Bernulli’s formula:

data:image/png;base64,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
data:image/png;base64,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
b) more than one
data:image/png;base64,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
c) at most one
data:image/png;base64,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