In a village of 2,500 people, 800 people are over 70 years old and 850

after solving this problem I learnt two things:
1) Reading the question well enough tells us what to solve for and avoids taking longer routes.
2) If we adopt an accounting approach via something like a double matrix here, it will become more challenging to solve this problem.

The question gives info on Females and population older than 70 years, but asks about a probability of males or younger. Well some arithmetic and probability we need to do.

P(male or <70 yrs) = Prob(male)+Prob(<70)-Prob(male and <70).
let us compute our sample space
n(male) = 2500-850 = 2550-900=1650.
Notice that second part is really number of female and <70 yrs = > 2/5*850= 340.
n of event space = 1650+340 = 1990.
prob = n of event space / number of entire population = 1990/2500 =>199/250.

2500 people

800 over 70

850 female

40% female younger than 70 = 850(0.4) = 340

850 - 340 = 510 greater than 70 for female

Males = 2500 - 850 = 1650

If 800 are greater than 70 and 510 females are greater than 70, then 800 - 510 = 290 males are greater than 70 years old.

1650 - 290 = 1360 males younger than 70

probability that a person chosen at random is either a male or younger than 70 years old:

(total males, which includes less than 70 years + females less than 70) = 1650 + 340 = 1990

1990/2500 = 199/250 B

or (males less than 70 + females less than 70 + males over 70) = 1360+340+290 = 1990

1990/2500 = 199/250 B

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