SOLUTION: 2. A group of randomly selected adults were asked if they are in favor of or against smoking. The following table gives the responses: In favor Against No opinion Male 445 37

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Question 1192081: 2. A group of randomly selected adults were asked if they are in favor of or against smoking. The following table gives the responses:
In favor Against No opinion
Male 445 370 120
Female 265 515 185
a. What is the most likely outcome?
b. One person is selected at random from these adults. Find the probability that this person is:
(i) In favor of smoking?
(ii) Female against smoking?
(iii) In favor of smoking given that the person is male
Answer by math_tutor2020(3817) About Me  (Show Source):
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Given Info:
In favorAgainstNo opinion
Male445370120
Female265515185


Part (a)

The most likely outcome is selecting a woman who is against smoking.
This is simply because the 515 is the largest value in the table corresponding to the parameters mentioned.

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Part (b)(i)

We have 445+265 = 710 people in favor of smoking.

This is out of 1900 people total (add up all the numbers to get 1900)

The probability we're after is 710/1900 = 71/190

Answer: 71/190

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Part (b)(ii)

There are 515 females against smoking which I mentioned back in part (a).

This is out of 1900 people total.

515/1900 = 103/380

Answer: 103/380
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Part (b)(iii)

The phrasing "given that the person is male" gives us prior knowledge to mean we only focus on the "male" row.

There are 445+370+120 = 935 males total
Of this subtotal, 445 males are in favor of smoking.

445/935 = 89/187

Answer: 89/187