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

Question

In a population of 100,000 males, 80% can be expected to live to age 60 and 60% can be expected to live to 80. Given that a male in this group is 60, what is the probability that he lives to 80?

A. 48%
B. 60%
C. 75%
D. 78%
E. 80%

pushpitkc · Accepted Answer

Of the 100000 males, there are 80000 males who make it to age 60.
Similarly, there are 60000 males who make it to age 80.

Since we are asked the probability of how many in the age of 60, make it to 80 :
 \frac{60000}{80000}*100 = 75%(Option C)

Bunuel · Answer

The wording is a bit confusing, and your confusion is understandable, but the question is asking for the conditional probability that a male who has already reached age 60 will live to 80. This isn’t a simple multiplication of probabilities but rather a conditional probability problem.

Here’s what the question says:

- 80% of males will live to at least 60.
- 60% of males will live to at least 80.

The question asks, if a male is 60 (so he’s already in the first group), what is the probability that he will live to 80 (thus reaching the second group)? So, the denominator would be 80%, and the numerator would be 60%.

The probability that a male lives to 80 given that he has already lived to 60 is:

P(lives \, to \, 80 \, | \, lives \, to \, 60) = \frac{P(lives \, to \, 80)}{P(lives \, to \, 60)} = \frac{0.60}{0.80} = 0.75

Or, simply, 80,000 men live to at least 60, and 60,000 of those, which is 3/4, live to at least 80. So, the probability is 3/4 = 0.75.

Answer: C.

Nunuboy1994 · Answer

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

ShashankDave · Answer

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

TimeTraveller · Answer

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.

chetan2u · Answer

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

JeffTargetTestPrep · Answer

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

Bharath.R · Answer

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.

Armaan209 · Answer

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%

Vibhatu · Answer

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%

bumpbot · Answer

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

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