A survey of TV viewing habits of 50 men and 50 women found the following information: Of the 50 men, 20 prefer watching baseball and 30 prefer football. Of the 50 women, 25 prefer watching baseball and 25 prefer football. Construct a data table for this data and answer this question: Out of the entire survey, what is the probability of choosing a woman who prefers baseball?
Men Women Total
prefer
baseball 20 25 45
prefer
football 30 25 55
Total 50 50 100
P(pf|W) = (25/100)/(50/100)
p = 25/50 = .5
Sure, here's a data table for the given information:
Gender | Baseball Preference | Football Preference
----------------------------------------------
Men | 20 | 30
Women | 25 | 25
To calculate the probability of choosing a woman who prefers baseball, we need to find the ratio of the number of women who prefer baseball to the total number of people in the survey. In this case, it would be 25 (women who prefer baseball) out of 100 (total number of people in the survey). So, the probability would be 25/100 which simplifies to 1/4. Therefore, the probability of choosing a woman who prefers baseball is 1/4.
To construct a data table, we can organize the information as follows:
TV Viewing Preferences | Men | Women | Total
------------------------ | --- | ----- | -----
Baseball | 20 | 25 | 45
Football | 30 | 25 | 55
To find the probability of choosing a woman who prefers baseball, we need to divide the number of women who prefer baseball by the total number of people in the survey.
Number of women who prefer baseball = 25
Total number of people in the survey = 100 (50 men + 50 women)
Therefore, the probability of choosing a woman who prefers baseball is 25/100 = 1/4 = 0.25 or 25%.
To construct a data table for the given information, we can organize it as follows:
| | Baseball | Football |
|------|----------|----------|
| Men | 20 | 30 |
| Women| 25 | 25 |
Now to answer the question:
To find the probability of choosing a woman who prefers baseball out of the entire survey, we need to know the total number of people surveyed and the number of women who prefer baseball.
From the given information, we know that there were 50 men and 50 women surveyed.
Out of the 50 women, 25 prefer baseball.
Therefore, the probability of choosing a woman who prefers baseball is:
(Number of women who prefer baseball) / (Total number of people surveyed)
= 25 / 100
= 0.25 or 25%
So, the probability of choosing a woman who prefers baseball out of the entire survey is 0.25 or 25%.