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

https://www.dartmouth.edu/~chance/teach ... apter4.pdf Refer to example 4.2

P(a) = 80 percent of the 100000 males, 80,000 males, can be expected to live to 60- but

P(b) = 60 percent of 100000 males, 60,000, males can be expected to live to

b is a subset of a so 60000/80000 * 100 = 75

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

Hello,

Sorry I fail to understand the question. My approach was to multiply the probabilities as the person in question is to be alive at 60 and 80.

80,000 live to 60
60,000 live to 80

That means 20,000 will not live to 80 or 1/4 will not live to 80

60,000 of 80,000 will live to 80 or 3/4 of 80,000 will live to 80

75%

This is a conditional Probability question:

Given that a man is belong to age 60 ground; probability he will live at age 60 is .6/.8= 75%