In a population of 100,000 males, 80% can be expected to live to age 6

Hi Bunuel. Please help me understand this.

Let me first write down the data given in the question, and for simplicity, I'm assuming tat there are 100 people.

By age 0
Alive = 100
Dead = 0

By age 60
Alive = 80
Dead = 20

By age 80
Alive = 60
Dead = 40


Now, consider the following questions and my understanding

What is the percentage of people who are already 60 will be alive at 80?

Answer = 60/80 = 75%

In how many ways can we select a person who is 60 years old and will be alive at 80?

Answer
\(\frac{60C1}{80C1}\)

75%

Now my understanding of the original question

If a person is randomly selected from people who are 60, what is the probability that he will live to 80?

In this case. we have first already selected a person, now this particular person can be a part of the 60 people who will live to 80, or of the 20 people who will not. We have to calculate the possibility that this particular person is a part of the 60 people who live and not of the 20 people who don't. How do we do that?
I know that I'm getting way too much confused here, but your answer to these questions will really help me understand probability 100%.

Thanks

No. of males that can live to age 60 = 80,000
No. of males that can live to age 80 = 60,000

Probability that a 60-year old male lives to 80 = 60,000/80,000 = 3/4. Ans - C.

Hi Shashank,

You have clearly understood the Q correctly even while answering and rewording the Q.
Now you pick up a person A who is part of gang of 80 person reaching 60years.
Now he can get into 60 person who do reach 80 years..
So probability is 60/80..
And this is exactly you have mentioned earlier

Since 80% and 60% are expected to live to ages 60 and 80, respectively, 80,000 and 60,000 males are expected to live to ages 60 and 80, respectively. Thus, the probability that a male lives to age 80, given that he is 60, is:

60,000/80,000 = 3/4 = 75%

Answer: C

what if he wasnt 60. what if he was 30, would the probability change?

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