In a village of 2,500 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?
Choose the most appropriate option
A) 221/250 B) 199/250 C) 33/50 D) 8/25 E) 51/250
To solve this we would need to know the number of people who are less than 70 years old, the number of males, and the number of males who are less than 70 years old.   Overlapping sets: quantity of A or 199/250 = A + 199/250 - (A∩199/250) = quantity of A + quantity of 199/250 - (intersection of A and 199/250)   Number of males = 2500-850= 
<gadget id="calculator">2500-850</gadget>
<output>1_650</output>
1650   Number of people below 70 years old= 2500-800= 
<gadget id="calculator">2500-800</gadget>
<output>1_700</output>
1700   Number of males below 70 years old= 1700-(850*0.4)= 
<gadget id="calculator">1700-(850*0.4)</gadget>
<output>1_360</output>
1360   Total number of people who are male OR below 70= 1650 + 1700 - 1360= 
<gadget id="calculator">1650 + 1700 - 1360</gadget>
<output>1_990</output>
1990   Probability of male or below 70= 1990/2500 = 199/250   Answer: 199/250
<result>B</result>
In a village of 2,500 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?