Question 1206350
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A sample of 75 people yielded the following information about their health insurance.
33 people with managed care plan
27 people with traditional insurance
15 people with no insurance
Two people who provided information for the table were randomly selected, without replacement. 
Determine the probability that neither had traditional insurance.
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        The solution by @Theo is incorrect.

        I came to bring a correct solution.



<pre>
First, we have 33 + 27 + 15 = 75.


Next, probability of the first person selected not having traditional insurance is {{{(75-27)/75}}} = {{{48/75}}}.

Probability of the second person selected not having traditional insurance is {{{47/74}}}.

Probability that both selected didn't have traditional insurance is {{{(48/75)*(47/74)}}} = 0.4065  (rounded).


<U>ANSWER</U>.  The probability that neither had traditional insurance is about 0.4065  (rounded).
</pre>

Solved.