Word Problem Probability

Question

In an island of 2,500 people, 800 people are over 60 years old and 850 people are female. It is known that 40 percent of the female are younger than 60 years old. If no one in the island is 60 years old, what is the probability that a person chosen at random is either a male younger or younger than 60 years old?

A. 199/250

B. 8/25

C. 221/250

D. 33/50

Answer 1

2500 people

800 people over 60

850 are female

40% of females are younger than 60

1. 60% of females are older than 60 which means that 510 of the females are over 60 and the remaining 340 females are younger than 60
2. We know 800 people are over 60 and if 510 of the females are over 60, that leaves 290 males that are over 60
3. We also know that the number of males are 2500 - 850 = 1650
4. The number of males under 60 must be 1650 - 290 = 1360
5. Therefore the probability that a person chosen at random is a male AND/OR younger than 60 is 1650 + 340 =1990/2500
6. This simplifies to 199/250 or A