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

Question

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.

Answer 1

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:

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:



b) more than one

c) at most one


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