Question

The following table shows the number of marriages in a given State broken down by age groups and gender:

                                                            AGE at the time of the marriage

	Less than 20	20-24		25-34	35-44	45 +	Total
Male	505	7,760		27,072	10,950	12,173
Female	1,252	11,405		27,632	9,651	10,352
Totals

Use the table to answer questions (1) to (11).

1. Use the information in the table to fill in the blanks in the row and column totals.
   

2. How many people (male and female) got married in the State?

3. If a person that was married was randomly chosen, what is the probability that the person was a female less than 20 years old? Express your answer as a percent rounded to the nearest whole percent.

4. If a person that was married was randomly chosen, what is the probability that the person was a male less than 20 years old? Express your answer as a percent rounded to the nearest whole percent.
5. If a person that was married was randomly chosen, what is the probability that the person was between the ages of 25 and 34? Express your answer as a percent rounded to the nearest whole percent.

6. Of the people over the age of 45 who got married, what percentage was female? What percentage was male? Express your answer as a percent rounded to the nearest whole percent.

7. Given that a person married was less than twenty years old, what is the probability that the person was male?

8. Given that a person married was female, what is the probability that the person was between the ages of 35 and 44?

9. If a person that was married was randomly chosen, what is the probability that the person was over the age of 45 or female?

10. If a person that was married was randomly chosen, what is the probability that the person is male and between the ages of 25 and 34?

11. Describe two events, A and B, which are mutually exclusive for the number of marriages in the State. Calculate the probability of each event, and the probability of A or B occurring.

Answer 1

                                                            AGE at the time of the marriage

	Less than 20	20-24		25-34	35-44	45 +	Total
Male	505	7,760		27,072	10,950	12,173	58460
Female	1,252	11,405		27,632	9,651	10,352	60292
Totals	1757		19165	54704	20601	22525	118752

Row and column data were added to fill Row and column totals

Number of people (male and female) got married in the State = 118752

If a person that was married was randomly chosen, the probability that the person was a female less than 20 years old

= Number of females less than 20 years old / Total number of people (male and female) got married in the State

= (1252 / 118752) * 100 %  = 1.05%

If a person that was married was randomly chosen, the probability that the person was a male less than 20 years old

= Number of males less than 20 years old / Total number of people (male and female) got married in the State

= (505 / 118752) * 100 %  = 0.43%

If a person that was married was randomly chosen, the probability that the person is between the ages of 25 and 34

= Number of persons between the ages of 25 and 34 / Total number of people (male and female) got married in the State

= (54704 / 118752) * 100 %  = 46.07%

Of the people over the age of 45 who got married, the percentage of female = Number of females over the age of 45 / Number of people over the age of 45

= (10352 / 22525) * 100 % = 45.96%

Of the people over the age of 45 who got married, the percentage of male = Number of males over the age of 45 / Number of people over the age of 45

= (12173 / 22525) * 100 % = 54.04%

Given that a person married was less than twenty years old, the probability that the person was male =

= Number of males less than twenty years old / Number of person less than twenty years old

= (505 / 1757) * 100 % = 28.74%

Given that a person married was female, the probability that the person was between the ages of 35 and 44

= Number of females between the ages of 35 and 44 / Number of females

= (9651 / 60292) * 100 % = 16.01%

Probability that the person was over the age of 45 or female

= Number of females or the ages over 45 / Number of Persons

= ((60292 + 22525 - 10352) / 118752) * 100 % = 61.02%