SOLUTION: 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 i

Question 1206350: 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:
A. Neither had traditional insurance.
Found 3 solutions by Theo, ikleyn, math_tutor2020:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
probability of the first person selected not having traditional insurance is 15/75.

probability of the second person selected not having traditional insurance is 14/74.

probability that both selected didn't have traditional insurance would be 15/75 * 14/74 = 210 / 5550

this simplifies to 7 / 185.

as a decimal, this is equal to .03784 when rounded to 5 decimal places.

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~

        The solution by @Theo is incorrect.
        I came to bring a correct solution.

First, we have 33 + 27 + 15 = 75. Next, probability of the first person selected not having traditional insurance is = . Probability of the second person selected not having traditional insurance is . Probability that both selected didn't have traditional insurance is = 0.4065 (rounded). ANSWER. The probability that neither had traditional insurance is about 0.4065 (rounded).

Solved.

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Tutor Theo seems to have mixed up "no insurance" with "not having traditional insurance". The second option could mean they have a managed health care plan or no insurance at all.

33 with managed care + 15 with no insurance = 48 people out of 75
48/75 = probability of selecting one such person
47/74 = probability of selecting another such person where the 1st person was not replaced

(48/75)*(47/74) = 376/925
376/925 = 0.406486486486 approximately
The "486" portion of the decimal repeats forever.

Answer
Exact fraction form = 376/925
Approximate decimal form = 0.406486486486
It's about a 40.65% chance of happening
Your teacher didn't state what format s/he wants the answer to be in, so you'll have to ask your teacher.

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